Answer
$\theta = 120^{\circ}$ or $300^{\circ}$
Work Step by Step
1. Since $cot\theta$ is negative, $\theta$ must be in quadrant II or IV.
2. The absolute value of $sec\theta$ is $\frac{\sqrt 3}{3}$, therefore the reference angles is $60^{\circ}$.
The actual angles in II and IV quadrants are following:
$180^{\circ}-60^{\circ}=120^{\circ}$
$180^{\circ}+60^{\circ}=300^{\circ}$
