JEE-Advanced 2015 (1/40)

Geometry Level 4

\[\large \frac{5}{4} \cos^2 2x+\cos^4 x+\sin^4 x+\cos^6 x+\sin^6 x=2\]

If \(x\) is a real number that satisfy the equation above, find the number of distinct solution(s) of \(x\) in the interval \([0,2\pi]\).

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