The whole problem is that it is not a 360 environment. If you look left, your player isn't looking left. If the player looks left when you do, then it creates a circle where you can't stop it and what you were looking at on the left would move to the tv. Then when you look back at the tv, the screen should rotate again.
They have to solve how to handle things off the screen. In a FPS, if you try to shoot someone on your right, will it allow you to shoot them even though your player is looking straight ahead? Do you have to track the bad guy from the wall to the tv until you can shoot him?

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