Answer
$120^o$
Work Step by Step
The value of $\theta$ must be in the interval $(0^o, 180^o) $.
$\theta=\cot^{-1}{\left(-\frac{\sqrt3}{3}\right)}$ means that $\cot{\theta} = -\frac{\sqrt3}{3}$.
Since cotangent is the reciprocal of tangent, then $\cot{\theta} = -\frac{\sqrt3}{3}$ means $\tan{\theta}=-\frac{3}{\sqrt3}=-\sqrt3$.
Note that $\tan{120^o} = -\sqrt3$.
Thus, $\cot^{-1}{\left(-\frac{\sqrt3}{3}\right)}=120^o$
