Answer
$150^\circ, 210^\circ$
Work Step by Step
Given $sec\theta=\frac{1}{cos\theta}=-\frac{2\sqrt 3}{3}$, we have $cos\theta=-\frac{\sqrt 3}{2}$, we can find a reference angle $\theta_0=acos(\frac{\sqrt 3}{2})=30^\circ$ and all values in $[0^\circ,360^\circ)$ as $\theta=150^\circ, 210^\circ$
