Solve $\displaystyle 2/(\cot {x}) + 3/(\csc {x}) = 0$, $\displaystyle 0<x<2\pi$.

After a few steps, I obtained

$\displaystyle (\sin {x})(2+3 \cos [x}) = 0$

$\displaystyle \sin {x} = 0$ or $\displaystyle \cos {x} = -2/3$

From $\displaystyle \sin {x} = 0$, I obtained the solution $\displaystyle x=\pi/2$. Is $\displaystyle x=\pi/2$ is a solution?