The sine of an angle is zero if and only if the angle is zero, with a periodicity of [tex]\pi[/tex]
In other words, you have
[tex]\sin(\alpha)=0\iff\alpha=0,\ \pm\pi,\ \pm 2\pi\ldots = k\pi,\ k\in\mathbb{Z}[/tex]
So, we have
[tex]\sin\left(\dfrac{2}{x}\right)=0 \iff \dfrac{2}{x}=k\pi \iff x =\dfrac{2}{k\pi}[/tex]
