Answer
$$\theta=20^\circ$$
Work Step by Step
$$\sin(3\theta-15^\circ)=\cos(\theta+25^\circ)\hspace{1cm}(1)$$
Cofunction identity:
$$\cos\theta=\sin(90^\circ-\theta)$$
So, $$\cos(\theta+25^\circ)=\sin[90^\circ-(\theta+25^\circ)]$$
$$\cos(\theta+25^\circ)=\sin(65^\circ-\theta)$$
Replace this in $(1)$ for $\cos(\theta+25^\circ)$:
$$\sin(3\theta-15^\circ)=\sin(65^\circ-\theta)$$
$$3\theta-15^\circ=65^\circ-\theta$$
$$4\theta=80^\circ$$
$$\theta=20^\circ$$
