# A nice Trignometric Series

Calculus Level 3

Let

$f(x) = \sin^{2} x - \frac{1}{2} \sin2x \times \sin^{2}x + \frac{1}{3} \sin3x \times \sin^{3}x - \ldots$

Then $\displaystyle f \left( \frac{\pi}{12} \right)$ can be written as

$\tan^{-1} \left( \dfrac{ a - \sqrt{b}}{c} \right)$

where $b$ is square free & $a,b,c \in\mathbb N$. Find the value of $a+b+c$.

×