Let y=y(x) be the solution of the differential equation cos x( log_e ( cos x))^2 d y+( sin x-3 y sin x log_e ( cos x)) d x=0, x ∈(0, (π)/2). If…

Let $\displaystyle y=y(x)$ be the solution of the differential equation $\displaystyle \cos x\left(\log _{\mathrm{e}}(\cos x)\right)^2 \mathrm{~d} y+\left(\sin x-3 y \sin x \log _{\mathrm{e}}(\cos x)\right) \mathrm{d} x=0, x \in\left(0, \frac{\pi}{2}\right)$. If $\displaystyle y\left(\frac{\pi}{4}\right)=\frac{-1}{\log _{\mathrm{e}} 2}$, then $\displaystyle y\left(\frac{\pi}{6}\right)$ is equal to :