13. $\sin 2 x+\cos 2 x+\sin x+\cos x+1=0$.

Translate the above text into English, keeping the original text's line breaks and format, and output the translation result directly.

13. $\sin 2 x+\cos 2 x+\sin x+\cos x+1=0$.
13. The equation is transformed into the form $(\sin x+\cos x)(2 \cos x+1)=0$.

From which $\quad x_{1}=\pi k-\frac{\pi}{4}, \quad x_{2}=2 \pi k \pm \frac{2}{3} \pi$.