Answer
$120^o$
Work Step by Step
The value of $\theta$ must be in the interval $[0^o, 90^o) \cup (90^o, 180^o] $.
$\theta=\sec^{-1}{(-2)}$ means that $\sec{\theta} = -2$.
Since secant is the reciprocal of cosine, then $\sec{\theta} = -2$ means $\cos{\theta}=-0.5$
Note that $\cos{120^o} = -0.5$.
Thus, $\sec^{-1}{\left(-2\right)}=120^o$
