Нужно решить уравнение (2sinx-корень2) (ctgx-корень 3) =0

Решите задачу:

$(2sinx-\sqrt2)(ctgx-\sqrt3)=0\\\\ \left[\begin{array}{ccc}2sinx-\sqrt2=0\\ctgx-\sqrt3=0\end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}2sinx=\sqrt2\\ctgx=\sqrt3\end{array}\right=\ \textgreater \ \left[\begin{array}{ccc}\displaystyle sinx=\frac{\sqrt2}2\\\\ctgx=\sqrt3\end{array}\right=\ \textgreater \ \\\\\\ =\ \textgreater \ \boxed{\left[\begin{array}{ccc}\displaystyle x=\frac{\pi}4+2\pi n;n\in Z\\\\\displaystyle x=\frac{3\pi}4+2\pi n;n\in Z\\\\\displaystyle x=\frac{\pi}6+\pi n;n\in Z\end{array}\right}$