JEE-Advanced 2015 (1/40)

Geometry Level 4

54cos22x+cos4x+sin4x+cos6x+sin6x=2\large \frac{5}{4} \cos^2 2x+\cos^4 x+\sin^4 x+\cos^6 x+\sin^6 x=2

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

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