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 $$[0,2\pi]$$.

×