Answer
$\theta$ = 40$^{\circ}$
Work Step by Step
$\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$)
According to Cofunction Identities
$\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$.
Therefore:
$\theta$ + (2$\theta$ - 30$^{\circ}$) = 90$^{\circ}$
3$\theta$ - 30$^{\circ}$ = 90$^{\circ}$
3$\theta$ = 120$^{\circ}$
$\theta$ = 40$^{\circ}$
