# Cos is nice

Geometry Level 5

$\cos^7 x + \cos^7 \left( x + \dfrac{2\pi}3 \right)+ \cos^7 \left( x + \dfrac{4\pi}3 \right) = 0 .$

Determine the number of roots of $x$ in the interval $[0,2\pi ]$ that satisfy the equation above.

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