Докажи тождество

\({\dfrac{\sin(\beta-\pi)\sin(2\pi-\beta)\cos(\beta-2\pi)}{\sin\left(\dfrac{\pi}{2}-\beta\right)\ctg(\pi-\beta)\ctg\left(\alpha+\dfrac{3\pi}{2}\right)}\raisebox{-1em}{\),\(}\mathrlap{\,=}}\) \({=\sin^{2}\beta}\) .