Answer
$236^{\circ}$
Work Step by Step
Given-
$\sec\theta$ = - $1.7876$ , $\theta$ belongs to Q III
We will find reference angle of $\theta$ first, using calculator in degree mode by the$\frac{1}{x}$ and $\cos^{-1}$ key with the positive value $1.7876$ as $\cos\theta$ = $\frac{1}{\sec\theta}$
$1.7876$ → $\frac{1}{x}$ → $\cos^{-1}$→→ 55.985045761
i.e. reference angle of $\theta$ = $55.985045761^{\circ}$
The desired angle $\theta$ is in Q III, whose reference angle is $55.985045761^{\circ}$.
Also $0^{\circ}\leq \theta\lt 360^{\circ}$
Therefore-
$\theta$ = $180^{\circ} + 55.985045761^{\circ}$
= $235.98504576^{\circ}$
= $236^{\circ}$
(to the nearest tenth of a degree)