Answer
$300^{\circ}$
Work Step by Step
Given-
$\sin\theta$ = - $\frac{\sqrt 3}{2}$ , $\theta$ belongs to Q IV
We will find reference angle of $\theta$ first using positive value $\frac{\sqrt 3}{2}$ and reference angle theorem-
$\sin\theta$ = - $\frac{\sqrt 3}{2}$ = -$\sin 60^{\circ}$ (As $\sin 60^{\circ}$ = $\frac{\sqrt 3}{2}$ )
Therefore by reference angle theorem, $60^{\circ}$ is the reference angle for desired angle $\theta$
The desired angle $\theta$ is in Q IV,
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $360^{\circ} - 60^{\circ}$
= $300^{\circ}$