Answer
$\theta$ = 18$^{\circ}$
Work Step by Step
$\sec$(3$\theta$ + 10$^{\circ}$) = $\csc$($\theta$ + 8$^{\circ}$)
$\sec$ and $\csc$ are cofunctions if the sum of the angles is 90$^{\circ}$
Therefore:
(3$\theta$ + 10$^{\circ}$) + ($\theta$ + 8$^{\circ}$) = 90$^{\circ}$
4$\theta$ + 18$^{\circ}$ = 90$^{\circ}$
4$\theta$ = 72$^{\circ}$
$\theta$ = 18$^{\circ}$
