13. Given $\tan \theta=2$, find the value of $\frac{\sin ^{2} \theta+2 \sin \theta \cos \theta}{\cos ^{2} \theta+\sin \theta \cos \theta}$.
13. $\frac{\sin ^{2} \theta+2 \sin \theta \cos \theta}{\cos ^{2} \theta+\sin \theta \cos \theta}=\frac{\tan ^{2} \theta+2 \tan \theta}{1+\tan \theta}=\frac{2^{2}+2^{2}}{1+2}=\frac{8}{3}$.