Answer
$135^{\circ}$
Work Step by Step
Given-
$\csc\theta$ = $\sqrt 2$ , $\theta$ belongs to Q II
We will find reference angle of $\theta$ first using value $\sqrt 2$ and reference angle theorem-
$\csc\theta$ = $\sqrt 2$ = $\csc 45^{\circ}$ (As $\csc 45^{\circ}$ = $\sqrt 2$)
Therefore by reference angle theorem, $45^{\circ}$ 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-
$\theta$ = $180^{\circ} - 45^{\circ}$
= $135^{\circ}$