# Tricky trigonometry question

Geometry Level 3

The value of $$\cos \left( \dfrac{\text{arctan}(4/3)}2 \right)$$ can be written as $$\pm \dfrac{a\sqrt b}c$$, where $$a$$, $$b$$ and $$c$$ are positive integers with $$b$$ square-free and $$a$$ and $$c$$ coprime. Find $$a+b+c$$.

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