Answer
$0$
Work Step by Step
1. $3(1-cos\theta)=sin^2\theta \Longrightarrow 3-3cos\theta=1-cos^2\theta \Longrightarrow cos^2\theta-3cos\theta+2=0 \Longrightarrow (cos\theta-2)(cos\theta-1)=0 \Longrightarrow cos\theta=2,1$,
2. $cos\theta=2 \Longrightarrow $ no solution in $[0,2\pi)$,
3. $cos\theta=1 \Longrightarrow \theta=0$ in $[0,2\pi)$.
