# 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.

###### This problem is part of the set Advent Calendar 2014.
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