Answer
$198^{\circ}$
Work Step by Step
Given-
$\sin\theta$ = - $0.3090$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first, using calculator in degree mode by the $\sin^{-1}$ key with the positive value $0.3090$-
$0.3090$ → $\sin^{-1}$→→ 17.998976188
i.e. reference angle of $\theta$ = $18^{\circ}$ (to the nearest degree)
The desired angle $\theta$ is in Q III, whose reference angle is $18^{\circ}$. Therefore-
$\theta$ = $ 180^{\circ} + 18^{\circ}$
= $198^{\circ}$