Day 14: Christmas is the Solution

Calculus Level 3

$C = \int_0^{3\pi} \bigg [ \frac{1 - \cos^2{\frac{x}{12}}} {1 - \sin^2{\frac{x}{12}}} + 1 \bigg ] \, \mathrm{d}x$ If the value of $2 + \frac{C}{144}$ is in the form $a/b$ where $a$ and $b$ are positive coprime integers and enter $a+b$ as your answer.

Day 14: Christmas is the Solution

This problem is part of the set Advent Calendar 2014.