Answer
$120^{\circ}$
Work Step by Step
Given-
$\sec\theta$ = - $2$ , $\theta$ belongs to Q II
We will find reference angle of $\theta$ first using value '$2$' and reference angle theorem-
$\sec\theta$ = - $2$ = - $\sec 60^{\circ}$ (As $\sec 60^{\circ}$ = $2$)
Therefore by reference angle theorem, $60^{\circ}$ is the reference angle for desired angle $\theta$
The desired angle $\theta$ is in Q II,
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} - 60^{\circ}$
= $120^{\circ}$