Answer
$30^\circ, 330^\circ$
Work Step by Step
1. From the given equation $-3sec\theta+2\sqrt 3=0$, we have $sec\theta=\frac{2\sqrt 3}{3}$ and $cos\theta=\frac{1}{sec\theta}=\frac{\sqrt 3}{2}$
2. For $\theta\in[0^\circ,360^\circ)$, we can find $\theta=30^\circ, 330^\circ$
