JEE Math Practice Question

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

1. A.$\frac{5-\sqrt{3}}{2 \sqrt{2}}$
2. B.$\frac{4 - \sqrt{2}}{14}$
3. C.$\frac{9\sqrt{3} + 3}{10(4 + \sqrt{3})}$
4. D.$\frac{\sqrt{3} + 1}{10(4 + \sqrt{3})}$