Answer
$\frac{\pi}{3}$, $\frac{5\pi}{3}$, $\frac{\pi}{2}$
Work Step by Step
$(2\cos \theta-1)(\sin \theta-1)=0$
If $2\cos \theta-1=0$, then $2\cos \theta=1$, and $\cos \theta=\frac{1}{2}$. The only solutions in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{5\pi}{3}$.
If $\sin \theta-1=0$, then $\sin \theta=1$, and the only solution in $[0, 2\pi)$ is $\frac{\pi}{2}$.
