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$cos(\frac{x}{3}+\frac{\pi}{6})=\frac{\sqrt2}{2}\\\\\frac{x}{3}+\frac{\pi}{6}=\pm \frac{\pi}{4}+2\pi n,\; n\in Z\\\\\frac{x}{3}=-\frac{\pi}{6}\pm \frac{\pi}{4}+2\pi n= \left \{ {{-\frac{\pi}{6}-\frac{\pi}{4}+2\pi n=-\frac{5\pi}{12}+2\pi n} \atop {-\frac{\pi}{6}+\frac{\pi}{4}+2\pi n=\frac{\pi}{12}+2\pi n}} \right. ,n\in Z\\\\x=-\frac{\pi}{2}\pm \frac{3\pi }{4}+6\pi n= \left \{ {{-\frac{5\pi}{4}+6\pi n} \atop {\frac{\pi}{4}+6\pi n}} \right. ,n\in Z$