Напишите в виде произведения:sina-sin(a+п/3) Зарание спасибо)))

Решите задачу:

$sin\alpha-sin(\alpha+\frac{\pi}{3} )=2*sin\frac{\alpha-(\alpha+\frac{\pi}{3})}{2}*cos\frac{\alpha+(\alpha+\frac{\pi}{3})}{2}=$ $2*sin(-\frac{\pi}{6})}*cos(\alpha+\frac{\pi}{6})=-2*sin(\frac{\pi}{6})}*cos(\alpha+\frac{\pi}{6})=-2*\frac{1}{2}}*cos(\alpha+\frac{\pi}{6})=-cos(\alpha+\frac{\pi}{6})=-(cos\alpha*cos\frac{\pi}{6}-sin\alpha*sin\frac{\pi}{6})=-(cos\alpha* \frac{ \sqrt{3} }{2} -sin\alpha*\frac{1}{2})= \frac{1}{2} *(sin\alpha-\sqrt{3}*cos\alpha)$