Answer
$\theta=30^{\circ},90^{\circ},150^{\circ}$
Work Step by Step
$2(\sin\theta)^{2}-3\sin\theta=-1$
$2(\sin\theta)^{2}-3\sin\theta+1=0$
$(\sin\theta-1)(2\sin\theta-1)=0$
$\sin\theta=1\,or\,\frac{1}{2}$
When $\sin\theta=1$, $\theta=90^{\circ}$
When $\sin\theta=\frac{1}{2}$, $\theta=30^{\circ},150^{\circ}$
So final answers are $30^{\circ},90^{\circ},150^{\circ}$.
