Solve for all possible theta in trigonometric equation tan t

Solve for all possible theta in trigonometric equation tan theta = sin 2 theta exactly over the interval 0 lessthanorequalto theta

Solution

Given

tan = sin 2

sin/cos = 2*sin*cos

1 = 2*cos^2

cos^2 = 1/2

cos = -1/sqrt(2) ==========> = 3pi/4, 5pi/4

cos = 1/sqrt(2) ==========> = pi/4, 7pi/4