Let \( y=y(x) \) be the solution of the differential equation \( \cos x(\log_e(\cos x))^2\,dy+(\sin x-3y\sin x\log_e(\cos x))\,dx=0 \), \( x\in\left(0,\frac{\pi}{2}\right) \). If \( y\left(\frac{\pi}{4}\right)=-\frac{1}{\log_e 2} \), then \( y\left(\frac{\pi}{6}\right) \) is equal to:
