Answer
$\theta=90^{\circ},270^{\circ}$
Work Step by Step
$3\cos\theta-2\sin\theta\cos\theta=0$
or, $\cos\theta(3-2\sin\theta)=0$
so, either $\cos\theta=0$ or $\sin\theta=\frac{3}{2}=1.5$
When $\cos\theta=0$,
$\theta=90^{\circ},270^{\circ}$ since $0\leq\,\theta\lt360$
$\sin\theta=1.5$ is not possible since $|\sin\theta|\leq1$
So, final solutions are $\theta=90^{\circ},270^{\circ}$
