Patron of the Arts
Watch a play in the Caf Thtre.

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In order to get plays to play out in the Cafe, you need to first complete all 5 Caf Thtre missions. They are fairly easy and nothing is too long or difficult. The first mission you get given to you as soon as you reach the Cafe; the rest you need to unlock. You do this by purchasing the renovations in the "Intendant's Study". There are 5 upgrades you need to buy. Once you have bought them all, you will have access to all the missions. Upon completing them all, plays will now continuously play out in the main room of the Cafe. All you need to do is walk close to the stage and watch the play. Not all plays seem to count towards the trophy though, so just stand there until it unlocks. Here is a visual walkthrough.