Answer
$\theta$ = 20$^{\circ}$
Work Step by Step
$\sec$($\theta$ + 10$^{\circ}$) = $\csc$(2$\theta$ + 20$^{\circ}$)
$\sec$ and $\csc$ are cofunctions if the sum of the angles is 90$^{\circ}$
Therefore:
($\theta$ + 10$^{\circ}$) + (2$\theta$ + 20$^{\circ}$) = 90$^{\circ}$
3$\theta$ + 30$^{\circ}$ = 90$^{\circ}$
3$\theta$ = 60$^{\circ}$
$\theta$ = 20$^{\circ}$
