Curtain Call at the Tampico

 is a quest in the Fallout: New Vegas add-on Dead Money.

Quick walkthrough
Where is the Holotape Projector?

- The Holotape Projector is up a staircase, overlooking the stage. If you are facing the stage, the staircase is to the right of the stage.

Where is the key to up stairs? The key is in Vera's Partitures. After Dean stops talking turn right, the first door you see is where you need to go. Its the one in the corner.

Where is the last holoprojector for the Hologram guard that patrols the stage? There is one right in the entrance hallway to the backstage, another one hidden behind a couch in the storage room backstage, but where is the third and final projector? After activating the projector the holograms disappear.

Do you have to kill Dean once you talk with him backstage? No you don't have to

Detailed walkthrough
as you enter into the theater go to the score sheet stand in front of the stage where you will find Vera Keyes' Partitures and a backstage key you will be immediately be confronted by Dean Domino. After ending your conversation 3 holograms will appear in the theater. Head quickly toward a closed door in the corner on the right from the stage. backstage there are three radios one in Dean's room, One on the wall in the Backstage closet and one in Vera's room. Go to Dean's room and pick up the key on the table. there is also a terminal opposite of the door to Vera's room that can disable the stage radio. Enter Vera's room and turn off the radio to your immediate right, pick up the holotape and the key underneath it. The key will open the door to the projector room opposite of the stage go up the stairs and play the tape in the projector the door to Dean is now open.

Behind the scenes
Curtain Call at the Tampico is actually a reference to the 1956 hit, "Smash that Tampico" by Sim Pinkett