Докажи тождество

\({\dfrac{\cos\alpha-2\cos\left(\dfrac{\pi}{3}+\alpha\right)}{2\sin\left(\alpha-\dfrac{\pi}{6}\right)-\sqrt{3}\sin\alpha}\raisebox{-2.5em}{\),\(}\mathrlap{\,=}}\) \({=-\sqrt{3}\tg\alpha}\) .