JEE Math Practice Question

Let $$y=y(x)$$ be the solution of the differential equation $$\frac{d y}{d x}=\frac{(\tan x)+y}{\sin x(\sec x-\sin x \tan x)}, x \in\left(0, \frac{\pi}{2}\right)$$ satisfying the condition $$y\left(\frac{\pi}{4}\right)=2$$. Then, $$y\left(\frac{\pi}{3}\right)$$ is

1. A.$$\sqrt{3}\left(2+\log _e 3\right)$$
2. B.$$\sqrt{3}\left(1+2 \log _e 3\right)$$
3. C.$$\sqrt{3}\left(2+\log _e \sqrt{3}\right)$$
4. D.$$\frac{\sqrt{3}}{2}\left(2+\log _e 3\right)$$