Решить уравнение sin х + cos х = -√2

Решите задачу:

$sinx+cosx=-\sqrt2|:\sqrt2\\\frac{\sqrt2}{2}sinx+cosx\frac{\sqrt2}{2}=-1\\\frac{\sqrt2}{2}=cos\frac{\pi}{4}, \; \frac{\sqrt2}{2}=sin\frac{\pi}{4}\\sinxcos\frac{\pi}{4}+cosxsin\frac{\pi}{4}=-1\\sin(x+\frac{\pi}{4})=-1\\x+\frac{\pi}{4}=-\frac{\pi}{2}+2\pi n\\x=-\frac{\pi}{4}-\frac{\pi}{2}+2\pi n\\x=-\frac{3\pi}{4}+2\pi n, \; n\in Z$