Find the exact solutions to the equation cos theta sin 2 th

Find the exact solutions to the equation cos theta - sin 2 theta = 0 in the interval [0, 2 pi]

Solution

cos theta - sin 2 theta=0

cos theta-2sin theta cos theta=0

cos theta(1-2sin theta)=0

cos theta=0 , 1-2sin theta=0

theta=pi/2 ,3pi/2 , theta=pi/6 , 5pi/6

theta=pi/6 ,pi/2,5pi/6,3pi/2