Question
If $f(x) = \frac{\sin^2 x}{1 + \cot x} + \frac{\cos^2 x}{1 + \tan x}$, then $f\left(\frac{\pi}{4}\right)$ is ______.
If $f(x) = \frac{\sin^2 x}{1 + \cot x} + \frac{\cos^2 x}{1 + \tan x}$, then $f\left(\frac{\pi}{4}\right)$ is ______.