If y(α) = 2( tanα + cotα 1 + ta n ^ 2 α ) + 1 si n ^ 2 α , α ∈...

Simplifying using Trigonometric Identity, we get,

$y\left(\alpha\right) = \left|1 + \cot \left(\alpha\right)\right|$

or, $y\left(\alpha\right) = - \left(1 + \cot \left(\alpha\right)\right)$, as $\alpha \in \left(\dfrac{3\pi}{4}, \pi\right)$

Hence, $\dfrac{dy}{d\alpha} = cose{c}^{2}\alpha$

${∴ \dfrac{dy}{d\alpha}}_{\alpha = \dfrac{5\pi}{6}} = 4$