Approach the cloak room on the left and talk to the guard there. You'll get an antique WWI pistol. Go to the toilet to the right of the cloak room and wait for one of the workers to enter. Be careful not to raise his suspicion or he'll leave. When he's using the toilet, sedate him and take his clothes. Put the body in the container to the right. You now have access to most parts of the level.
Leave the toilet, go around the cloak room and go through the door to the left of it. Go down the stairs and past the carpenter. When you enter a bigger room, you'll see two workers having a break there. Wait until they get back to work and pick the lock in the door ahead when neither of them is watching. When you're in a long corridor, use the first door to the right. You'll eventually see a door with a golden star by it. That's not the one you want - find the one with the silver star (to the right of the golden one) and enter when the bodyguard is away. Enter the closet and wait for one of the actors to come here. It might take a while, but there's nothing you can do about it. When he enter, he'll say a few lines facing the mirror and leave for the toilet. Quickly leave the closet and swap the gun he left with the one you have in your inventory. Malevolent, isn't it?
Go back to the closet and wait for the actor to return and take the gun. When he's out, leave the room at last and go through the door just across the corridor. Go up to the light controls. Go past the worker to the next room and place a bomb at the device shown at the screenshot below.
Now you're ready. Go back to where you left your original suit and wear it, then go to the main room of the opera and watch what happens. The actor will be shot using the gun you replaced. When everyone realizes something's not right, your second target will run down to the stage. When he's running though the audience, he'll fall down for a brief moment. When he's down, detonate the bomb. Checkmate - leave the opera and be proud.