If $x=f(y)$ is the solution of the differential equation $$ \left(1+y^2\right)+\left(x-2 \mathrm{e}^{\tan ^{-1} y}\right) \frac{\mathrm{d} y}{\mathrm{~d} x}=0, y \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right) $$ with $f(0)=1$, then $f\left(\frac{1}{\sqrt{3}}\right)$...