#### Answer

$\theta=15^{\circ}$

#### Work Step by Step

Since sine and cosine are cofunctions, $\sin(\theta+15^{\circ})= cos (2\theta+30^{\circ})$ is true if the sum of the angles is 90°.
$(\theta+15^{\circ})+(2\theta+30^{\circ})=90^{\circ}$
$3\theta+45^{\circ}=90^{\circ}$
Subtracting $45^{\circ}$ from each side, $3\theta=45^{\circ}$
Dividing each side by $15$, $\theta=15^{\circ}$