Answer
$\theta$ = 12$^{\circ}$
Work Step by Step
$\cot$(5$\theta$ + 2$^{\circ}$) = $\tan$(2$\theta$ + 4$^{\circ}$)
$\tan$ and $\cot$ are cofunctions if the sum of the angles is 90$^{\circ}$
Therefore:
(5$\theta$ + 2$^{\circ}$) + (2$\theta$ + 4$^{\circ}$) = 90$^{\circ}$
7$\theta$ + 6$^{\circ}$ = 90$^{\circ}$
7$\theta$ = 84$^{\circ}$
$\theta$ = 12$^{\circ}$
