If I(x) = ∫ 6dx / sin^2 x(1+cot x)^2 and I(0) = 3 then

Question

If I(x) = \(\int \frac{6dx}{sin^2 x(1+cot\,x)^2}\) and I(0) = 3 then \(I(\frac {\pi}{12})\) is equal to

(1) \(\frac {21 -9\sqrt {3}}{3-\sqrt {3}}\)

(2) \(\frac {21 +9\sqrt {3}}{3-\sqrt{3}}\)

(3) \(\frac {21}{3-\sqrt {3}}\)

(4) \(\frac {3+\sqrt {3}}{3-\sqrt {3}}\)

Answer 1

Correct option is (1) \(\frac {21 -9\sqrt {3}}{3-\sqrt {3}}\)