Quadripple

In a dark dark room, four identical coins lie on a square table in the corners. The sides of each coin are painted in two colors - red and blue, there are no other differences between the sides. If all the coins are lying with the same color facing up, a light comes on above the table, otherwise the room is completely dark. The player can turn over (at once) any set of coins in one move, after which either the light comes on, or the table rotates at an arbitrary angle and the game continues.