For \( x \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right) \), if \( y(x) = \int \frac{cosec x + \sin x}{cosec x \sec x + \tan x \sin^2 x} \, dx \), and \( \displaystyle \lim_{x \to \left( \frac{\pi}{2} \right)^{-}} y(x) = 0 \) then \( y\left( \frac{\pi}{4} \right) \) is equal to:
