Om tre dage skal jeg i teatret med min søster, og vi har glædet os siden vi købte billetterne for en måned siden.

This is because Danish follows the V2 rule in main clauses: the finite verb usually comes in the second position.

So when the sentence starts with the time expression Om tre dage, that counts as the first element, and the verb skal must come next:

• Om tre dage = first element
• skal = second element
• jeg = comes after the verb

That is why Danish says:

• Om tre dage skal jeg i teatret ...

and not:

• Om tre dage jeg skal i teatret ...

This is very common in Danish whenever you move a time phrase, place phrase, or other adverbial to the front.

For comparison:

• Jeg skal i teatret om tre dage.
• Om tre dage skal jeg i teatret.

Both are correct, but the second one emphasizes the time.

Om tre dage means in three days.

It refers to a point in the future, counted from now.

A learner often mixes this up with other time expressions:

• om tre dage = in three days
• i tre dage = for three days
• efter tre dage = after three days

Examples:

• Om tre dage rejser vi. = We leave in three days.
• Vi rejste i tre dage. = We traveled for three days.
• Efter tre dage kom han tilbage. = After three days, he came back.

So in your sentence, Om tre dage tells you when the trip to the theatre will happen.

Skal can mean must, but it can also be used for a planned future event.

In this sentence, skal does not mainly mean obligation. It sounds more like:

• am going to
• will
• am supposed to

Because the tickets were already bought, the event is clearly planned. So skal fits very naturally.

So:

• Om tre dage skal jeg i teatret ...

means something like:

• In three days I’m going to the theatre ...

It suggests a firm arrangement, not just a vague future idea.

In Danish, gå i teatret is a very common idiomatic expression meaning to go to the theatre as an activity, usually to see a performance.

So:

• jeg skal i teatret = I’m going to the theatre

Here, i is the natural choice.

By contrast, til teatret can sound more like movement toward the building as a destination. It is not always wrong, but i teatret is the standard expression when talking about attending the theatre.

This is similar to other Danish expressions where the preposition does not match English exactly.

Because Danish often marks definiteness by adding the article to the end of the noun.

For teater:

• et teater = a theatre
• teatret = the theatre

So i teatret literally means in the theatre / at the theatre, but in this context it means to the theatre as an event.

This is one of the big differences from English: instead of putting the before the noun, Danish often attaches it to the noun.

Billetterne is the definite plural form:

• en billet = a ticket
• billetter = tickets
• billetterne = the tickets

The definite form is used because these are specific tickets already known in the context: the ones they bought for the theatre trip.

So:

• vi købte billetterne = we bought the tickets

Even though English might sometimes say we bought tickets, Danish often prefers the definite form when the tickets are understood to be for that particular event.

Because in Danish, a possessive normally replaces the definite article.

So you say:

• min søster = my sister
• min billet = my ticket
• vores billetter = our tickets

You do not usually combine min with a suffixed definite article like -en or -et.

So:

• min søster = correct
• min søsteren = incorrect

This works much like English, where you say my sister, not my the sister.

Because the first part talks about the speaker alone, and the second part refers to the speaker and the sister together.

• jeg = I
• vi = we

So:

• Om tre dage skal jeg i teatret med min søster
  = In three days I’m going to the theatre with my sister

Then:

• og vi har glædet os ...
  = and we have been looking forward to it ...

Once the sister is included, the subject naturally becomes we.

The verb is glæde sig, which is a reflexive verb.

That means it uses a reflexive pronoun:

• jeg glæder mig
• du glæder dig
• han/hun glæder sig
• vi glæder os

So os is there because the subject is vi.

In this sentence:

• vi har glædet os
  means
• we have been looking forward to it
  or
• we have been excited about it

This is important: glæde sig is not usually translated word-for-word. Literally it looks like to gladden oneself, but idiomatically it often means to look forward to something.

Because the two actions have different time meanings.

• har glædet os is present perfect
• købte is simple past

This makes sense because:

1. The looking forward started in the past and continues up to now
   → so Danish uses har glædet os

2. The buying happened once at a specific moment in the past
   → so Danish uses købte

So the structure means:

• We bought the tickets a month ago.
• From that point until now, we have been looking forward to the event.

That is why the tense combination is very natural in Danish.

They look similar in English, but they do different jobs in Danish.

• siden = since
• for en måned siden = a month ago

In the sentence:

• vi har glædet os siden ...
  = we have been looking forward to it since ...

• for en måned siden
  = a month ago

So the whole phrase:

• siden vi købte billetterne for en måned siden

means:

• since we bought the tickets a month ago

This can feel confusing because Danish uses siden in one place and for ... siden in another, but they are not the same expression.

Because Danish often leaves the object understood when it is obvious from the context.

Here, what they are looking forward to is clearly the trip to the theatre. So Danish does not need to spell it out.

You could make it more explicit in other sentences, for example:

• Vi har glædet os til forestillingen. = We have been looking forward to the performance.

But in your sentence, it is enough to say:

• vi har glædet os

because the meaning is already clear from the rest of the sentence.