Let \(y=y(x)\) be a solution curve of the differential equation \((y+1) \tan ^2 x d x+\tan x d y+y d x=0, x \in\left(0, …

Let \(y=y(x)\) be a solution curve of the differential equation \((y+1) \tan ^2 x d x+\tan x d y+y d x=0, x \in\left(0, \frac{\pi}{2}\right)\). If \(\lim _{x \rightarrow 0^{+}} x y(x)\) \(=1\), then the value of \(y\left(\frac{\pi}{4}\right)\) is:

[JEE Main 2021, 26 Aug (Shift 1)]