Answer
$150^{\circ}$
Work Step by Step
Given-
$\csc\theta$ = $2$ , $\theta$ belongs to Q II
We will find reference angle of $\theta$ first using value '$2$' and reference angle theorem-
$\csc\theta$ = $2$ = $\csc 30^{\circ}$ (As $\sec 60^{\circ}$ = $2$)
Therefore by reference angle theorem, $30^{\circ}$ 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-
$\theta$ = $180^{\circ} - 30^{\circ}$
= $150^{\circ}$