Answer
See proof below.
Work Step by Step
Apply the sum formula:
$\sin(A+B)=\sin(A)\cos(B)+\cos(A)\sin(B)$
In order to prove the given identity, we simplify the left hand side $\text{LHS}$ as follows:
$\text{LHS } =\sin(\pi - \theta)
\\=\sin (\pi) \cos (\theta) +\cos \pi \sin(\theta)
\\=(0)( \cos(\theta)) +(-1) (\sin(\theta))
\\=-\sin (\theta)\\=\text{ RHS}$
