#### Answer

$260.54^{\circ}$

#### Work Step by Step

Here, we have $\sin^{-1} (6)$
The angle $\theta$ is in the First quadrant.
This means that
$\theta=\tan^{-1} (6) \approx 80.54^{\circ}$
We want an angle in the Third quadrant:
Then we have $\theta=\theta'+180^{\circ}=80.54^{\circ}+180^{\circ}=260.54^{\circ}$