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