2. Given that $x, y$ are positive numbers, and $\frac{\sin \theta}{x}=\frac{\cos \theta}{y}, \frac{\cos ^{2} \theta}{x^{2}}$ $+\frac{\sin ^{2} \theta}{y^{2}}=\frac{10}{3\left(x^{2}+y^{2}\right)}$. Then the value of $\frac{x}{y}$ is $\qquad$.
$2 . \sqrt{3}$ or $\frac{1}{\sqrt{3}}$