Answer
$\theta=3^{\circ}$
Work Step by Step
1. Cosecant and sine are reciprocals
$\csc\theta=\frac{1}{\sin\theta}$
2. Rewrite cosencant as a sine
$\sin(4\theta +2^{\circ})=\sin(3\theta+5^{\circ})$
3.Since the sine values are equal, the angles themselves must be equal.
$4\theta -3\theta= 5-2$
$\theta=3^{\circ}$
