JEE Math Practice Question

Let ƒ(x) = (sin(tan–1x) + sin(cot–1x))2 – 1, |x| > 1. If $${{dy} \over {dx}} = {1 \over 2}{d \over {dx}}\left( {{{\sin }^{ - 1}}\left( {f\left( x \right)} \right)} \right)$$ and $$y\left( {\sqrt 3 } \right) = {\pi \over 6}$$, then y($${ - \sqrt 3 }$$) is equal to :

1. A.$${{5\pi } \over 6}$$
2. B.$$ - {\pi \over 6}$$
3. C.$${\pi \over 3}$$
4. D.$${{2\pi } \over 3}$$