`sin (2x +pi/3)=-\sqrt{2}/2`

`<=> sin (2x +pi/3)=sin(-pi/4)`

`<=>` $\left[\begin{matrix} 2x+\dfrac{\pi}{3}=-\dfrac{\pi}{4}+k2\pi\\ 2x+\dfrac{\pi}{3}=\pi+\dfrac{\pi}{4}+k2\pi\end{matrix}\right.$ `(k in ZZ)`
`<=>` $\left[\begin{matrix} 2x=-\dfrac{7\pi}{12}+k2\pi\\ 2x=\dfrac{11\pi}{12}+k2\pi\end{matrix}\right.$
`<=>` $\left[\begin{matrix} x=-\dfrac{7\pi}{24}+k\pi\\ x=\dfrac{11\pi}{24}+k\pi\end{matrix}\right.$

Vậy $x=-\dfrac{7\pi}{24}+k\pi$ hoặc $x=\dfrac{11\pi}{24}+k\pi$