Solve the equation on the interval 02pi 9 sin2theta sinthet

Solve the equation on the interval [0,2pi)

9) sin2theta + sintheta=0

Solution

sin 2 theta + sin theta=0

2 sin theta cos theta + sin theta=0

sin theta(2 cos theta +1)=0

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

theta=sin^-10 , theta=cos^-1(-1/2)

theta=0,pi   , theta= 2pi/3, 4pi/3

theta=0,2pi/3, pi, 4pi/3