Sine - Future and Past

If the integral $\displaystyle I = \int \limits_0^{\pi /12084} \sin (2015 x) \sin ^{2013} x \text{ d}x$ can be expressed as $\displaystyle \frac{1}{c} . \bigg( \frac{\pi }{a} \bigg)^b$ , where $a,b$ and $c$ are natural numbers.

Evaluate: $\displaystyle \frac{ac}{b^2}$

Details and Assumptions:

• $\displaystyle \sin x = x$ for small $x$ .