Answer
Please refer to the step-by-step part below.
Work Step by Step
Use the identity $\sin{(\alpha+\beta)}=\sin{(\alpha)}\cos{(\beta)}+\cos{(\alpha)}\sin{(\beta)}$ to obtain:
$\sin{(\pi+\theta)}\\
=\sin{(\pi)}\cos{(\theta)}+\cos{(\pi)}\sin{(\theta)}\\=0\cos{(\theta)}+(-1)\cdot \sin{(\theta)}\\=-\sin{(\theta)}$
