If y(α)=√(2((tan α+ cot α)/(1+ tan^2 α))+1/(sin^2 α)), α ∈((3 π)/4, π), then (d y)/(d α) at α=(5 π)/6 is:

If $$y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^2 \alpha}\right)+\frac{1}{\sin ^2 \alpha}}, \alpha \in\left(\frac{3 \pi}{4}, \pi\right), $$ then $\displaystyle \frac{\mathrm{d} y}{\mathrm{~d} \alpha}$ at $\displaystyle \alpha=\frac{5 \pi}{6}$ is :