Finding the smallest positive and the largest negative coterminal angle in standard position.

225 degrees is 225 - 360 = -135, 225 + 360 = 585.
412 degrees is 412 - 360 = 52, 52 - 360 = 308.
I don't understand why 412 degrees is 412 - 360 = 52, 412 + 360 = 772. Can you explain in detail?

In the 412 case we have alread y exceeded one 360 so the smallest positive that is coterminal is 412 - 360 = 52 degrees
then we take another 360 away:
52 - 360 = - 308 degrees for the negative coterminal