Answer:
[tex]\large\boxed{x=\dfrac{5\pi}{4}\ \vee\ x=\dfrac{7\pi}{4}}[/tex]
Step-by-step explanation:
The first step in attachment.
[tex]\sin(x)=-\dfrac{\sqrt2}{2}\to x=-\dfrac{\pi}{4}+2k\pi\ \vee\ x=\dfrac{5\pi}{4}+2k\pi\\\\x\in[0,\ 2\pi)\\\\\text{Therefore}\\\\x=-\dfrac{\pi}{4}+2\pi=\dfrac{7\pi}{4}\ \vee\ x=\dfrac{5\pi}{4}[/tex]
