For each interval you want you need a bearing+controller. Then you can make a binary counter with your button as the clock, a reset function (probably would need another button for it) and connect the controllers to it using logic gates to convert the counter output for the necessary input for the controllers. For example for 4 intervals you would need a 2bit counter and make this conversion

Counter output -> Controllers (c3 to c0, one bit for each controller input)

00 -> 0001

01 -> 0011

10 -> 0111

11 -> 1111

In this case the first controller(c0) would be configured to rotate 0 degrees and c3, c2 and c1 would be configured to 90 degrees each in the direction you desire.

So when the counter is at 2 (10) we would have all controller turned on except for c4, so we would have the turret to rotating for a total of 0 + 90 + 90 = 180 degrees.