`sin(3x-\pi/6)=-\sqrt3/2`
`<=>sin(3x-\pi/6)=sin(-\pi/3)`
`<=>`\(\left[ \begin{array}{l}3x-\dfrac{\pi}6=-\dfrac{\pi}3+k2\pi\\3x-\dfrac{\pi}6=\dfrac{4\pi}3+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}3x=-\dfrac{\pi}6+k2\pi\\3x=\dfrac{3\pi}2+k2\pi\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=-\dfrac{\pi}{18}+\dfrac{k2\pi}3\\x=\dfrac{\pi}2+\dfrac{k2\pi}3\end{array} \right.\ (k\in \Bbb Z)\)
