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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