Answer
$\theta$ lies in quadrant II
Work Step by Step
Given
$\csc\theta \gt 0$ i.e. $\csc\theta$ is positive.
$\cos\theta \lt 0$ i.e. $\cos\theta$ is negative.
$\csc$ is positive and $\cos$ is negative in quadrant II only, therefore-
$\theta$ lies in quadrant II
