Answer
$240^{\circ}$
Work Step by Step
Given-
$\tan\theta$ = $\sqrt 3$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first using value $\sqrt 3$ and reference angle theorem-
$\tan\theta$ = $\sqrt 3$ = $\tan 60^{\circ}$ (As $\tan 60^{\circ}$ = $\sqrt 3$)
Therefore by reference angle theorem, $60^{\circ}$ is the reference angle for desired angle $\theta$
The desired angle $\theta$ is in Q III,
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} + 60^{\circ}$
= $240^{\circ}$