Calculus: Early Transcendentals, Chapter 4, 4.1, Section 4.1, Problem 41

You need to find the critical points of the function, hence, you need to evaluate the solutions to the equation f'(theta) = 0 .
You need to evaluate the first derivative:
f'(theta) = -2 sin theta + 2sin theta*cos theta
You need to solve for theta f'(theta) = 0 , such that:
-2 sin theta + 2sin theta*cos theta= 0
Factoring out 2sin theta yields:
2sin theta*(-1 + cos theta) = 0
Put 2sin theta = 0 => sin theta = 0
theta = (-1)^k*arcsin 0 + kpi
theta = kpi
Put -1 + cos theta= 0 =>cos theta = 1
theta = +-arccos 1 + 2kpi
theta = 2kpi
Hence, evaluating the critical numbers of the function for f'(theta) = 0 , yields theta =2kpi, theta = kpi.