If for the solution curve \(y=f(x)\) of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+(\tan x) y=\frac{…

If for the solution curve \(y=f(x)\) of the differential equation \(\frac{\mathrm{d} y}{\mathrm{~d} x}+(\tan x) y=\frac{2+\sec x}{(1+2 \sec x)^2}\), \(x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right), f\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{10}\), then \(f\left(\frac{\pi}{4}\right)\) is equal to :

[JEE Main 2025, 29 Jan (Shift 2)]