(1 + cos4x) sin2x >= cos^2 2x

2cos^2 2x × sin2x - cos^2 2x >=0

cos^2 2x(2sin2x - 1)>= 0

cos^2 2x >= 0, x € R

2sin2x >= 1

sin2x >= 1/2

π/6 + 2πk =< 2x =< 5π/6 + 2πk

π/12 + πk =< x =< 5π/12 + πk ; k € Z

x € [π/12 + πk ; 5π/12 + πk] ; k € Z