Let y=y(x) be a solution curve of the differential equation

$(y+1) \tan ^{2} x d x+\tan x d y+y d x=0$

or $\frac{d y}{d x}+\frac{\sec ^{2} x}{\tan x} \cdot y=-\tan x$

$I F=e^{\int \frac{\sec ^{2} x}{\tan x} d x}=e^{\ln \tan x}=\tan x$

$\therefore y \tan x=-\int \tan ^{2} x d x$

or $y \tan x=-\tan x+x+C$

or $y=-1+\frac{x}{\tan x}+\frac{C}{\tan x}$

or $\lim _{x \rightarrow 0} x y=-x+\frac{x^{2}}{\tan x}+\frac{C x}{\tan x}=1$

or $\mathrm{C}=1$

$y(x)=\cot x+x \cot x-1$

$y\left(\frac{\pi}{4}\right)=\frac{\pi}{4}$