Learn Italian: Aggiunto il ciondolo, dovevamo fissare il gancio. - Having added the pendant, we had to attach the clasp.

This is the Absolute Past Participle. It is a concise way to express 'After something was done' or 'Having done something'. You could also say Dopo aver aggiunto il ciondolo, but this absolute construction is very common in Italian and sounds a bit more elegant.

Does aggiunto have to agree with the noun il ciondolo?

Yes! In the Absolute Past Participle construction, the past participle acts almost like an adjective and must agree in gender and number with the noun it refers to. Since il ciondolo is masculine singular, we use aggiunto. If we had added a pearl (la perla), it would be Aggiunta la perla.

What is the infinitive of aggiunto and is it irregular?

It is the irregular past participle of the verb aggiungere (to add). As a handy tip, most Italian verbs ending in -giungere follow this same pattern and end in -giunto for their past participle, such as raggiungere (to reach) becoming raggiunto.

Why use the imperfect dovevamo instead of the passato prossimo (abbiamo dovuto)?