# I Dare You To Take A Special Case! Part 2

Geometry Level 5

Let $$\Gamma_1$$ be the circumcircle of $$\Delta ABC$$ and $$\Gamma_2$$ be the circumcircle of $$\Delta DEF$$ where $$D,E,F$$ are the foot of the altitudes of $$\Delta ABC$$.

If $$\Gamma_1$$ cuts $$\Gamma_2$$ orthogonally, compute the value of the following expression upto three decimal places:

$\sum_\text{cyc} \cos 2A$

Notations:

• $$A$$ denotes $$\angle BAC$$. $$B$$ and $$C$$ are defined similarly.
• $$\displaystyle \sum_\text{cyc}$$ denotes cyclic summation.

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