2 sin (x + П/6) = -1

[latex]2sin(x+ \frac{\pi}{6} )=-1\\sin(x+ \frac{\pi}{6} )=- \frac{1}{2}\\ x+\frac{\pi}{6}=- \frac{ \pi }{6}+2\pi*k\\x=- \frac{ \pi }{3}+2pik [/latex],k∈z