Answer
$\theta$ = 12$^{\circ}$
Work Step by Step
$\tan$(3$\theta$ + 4$^{\circ}$) = $\cot$(5$\theta$ - 10$^{\circ}$)
$\tan$ and $\cot$ are cofunctions if the sum of the angles is 90$^{\circ}$
Therefore:
(3$\theta$ + 4$^{\circ}$) + (5$\theta$ - 10$^{\circ}$) = 90$^{\circ}$
8$\theta$ - 6$^{\circ}$ = 90$^{\circ}$
8$\theta$ = 96$^{\circ}$
$\theta$ = 12$^{\circ}$
