If x = f(y) is the solution of the differential equation (1 + y²) + (x - 2e^{tan-1 y})\(\frac{\mathrm{dy}}{\mathrm{dx}}\) = 0, y ∈ \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\) with f(0) = 1, then f\(\left(\frac{1}{\sqrt{3}}\right)\)  is equal to :