Let $y=y(x)$ be the solution of the differential equation $x \frac{\mathrm{~d} y}{\mathrm{~d} x}-y=x^2 \cot x, x \in(0, \pi)$. If $y\left(\frac{\pi}{2}\right)=\frac{\pi}{2}$, then $6 y\left(\frac{\pi}{6}\right)-8 y\left(\frac{\pi}{4}\right)$ is equal to:
