# Waiting for 2016 - 2

Geometry Level 5

$\large \dfrac{4\sqrt{7}}{3} \cos \left(\dfrac{1}{3} \arccos \left(\dfrac{1}{\sqrt{28}} \right) \right) + \dfrac{1}{3}$

The expression above can be simplified into the form

$\large a \left(\cos \left(\dfrac{b \pi}{e} \right) +\cos \left(\dfrac{c \pi}{e} \right)+\cos \left(\dfrac{d \pi}{e} \right) \right)$

where $$a,b,c,d$$ and $$e$$ are positive integers with $$\gcd(b,e) = \gcd(c,e) = \gcd(d,e) = 1$$.

If all the angles mentioned above lie in the interval $$[ 0, \pi ]$$, find the value of $$a+b+c+d+e$$..

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