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