If \( x=f(y) \) is the solution of the differential equation \(\displaystyle (1+y^{2})+(x-2e^{\tan^{-1}y})\frac{dy}{dx}=0, \; y \in \left(-\frac{\pi}{2},\frac{\pi}{2}\right) \) with \( f(0)=1 \), then \(\displaystyle f\!\left(\frac{1}{\sqrt{3}}\right) \) is equal to:
