# Trigo!

Geometry Level 4

If $$A$$, $$B$$ and $$C$$ are positive such that $$A+B+C = \pi$$. Find for which value of $$A$$, $$B$$ and $$C$$ that minimizes the following.

$\large \frac{\cos \left(\frac{A-B}{2}\right)}{\cos \left(\frac{A+B}{2}\right)} + \frac{\cos \left( \frac{B-C}{2}\right)}{\cos \left(\frac{B+C}{2}\right)} + \frac{\cos \left(\frac{C-A}{2}\right)}{\cos \left(\frac{C+A}{2}\right)}$

If the answer is of the form $$\dfrac{a \pi}{b}$$, find $$a+b$$, where $$a$$ and $$b$$ are coprime positive integers.

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