Answer
$\theta$ = 35$^{\circ}$
Work Step by Step
$\csc$($\theta$ + 40$^{\circ}$) = $\sec$($\theta$ - 20$^{\circ}$)
$\sin$ and $\cos$ are cofunctions of each other assuming that the sum of the angles equals 90$^{\circ}$
($\theta$ + 40$^{\circ}$) + ($\theta$ - 20$^{\circ}$) = 90$^{\circ}$
2$\theta$ + 20$^{\circ}$ = 90$^{\circ}$
2$\theta$ = 70$^{\circ}$
$\theta$ = 35$^{\circ}$
