# Trigonometry or elementary algebra?

Geometry Level 5

$\large \sqrt[3]{\cos\left( \frac{2\pi}{7} \right)} + \sqrt[3]{\cos \left(\frac{4\pi}{7}\right)} + \sqrt[3]{\cos \left(\frac{8\pi}{7}\right)}$

If the value of the trigonometric expression above equals to $\displaystyle \large \sqrt[3]{\frac{1}{d}( a - b\sqrt[b]{c})}$ where $$a,b,c$$ and $$d$$ are positive integers, find the value of $$a+b+c+d$$.

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