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