If \( y(\alpha)=\sqrt{2\left(\frac{\tan \alpha+\cot \alpha}{1+\tan ^{2} \alpha}\right)+\frac{1}{\sin ^{2} \alpha}}, \alp…

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 \( \frac{\mathrm{dy}}{\mathrm{d} \alpha} \) at \( \alpha=\frac{5 \pi}{6} \) is

[JEE Main 2020, 7 Jan (Shift 1)]