Answer
$0,\pi,\frac{\pi}{3},\frac{5\pi}{3}$
Work Step by Step
1. $tan\theta=2sin\theta \Longrightarrow \frac{sin\theta}{cos\theta}=2sin\theta \Longrightarrow sin\theta=0,\ or\ cos\theta=\frac{1}{2}$,
2. $sin\theta=0 \Longrightarrow \theta=0,\pi$ in $[0,2\pi)$,
2. $cos\theta=\frac{1}{2} \Longrightarrow \theta=\frac{\pi}{3},\frac{5\pi}{3}$ in $[0,2\pi)$.
