JEE Math Practice Question

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

1. A.4
2. B.-4
3. C.$${4 \over 3}$$
4. D.-$${1 \over 4}$$