#4cos^2x-sin^2 2x+color(red)(5)sin^2x=4#.
#:. 4cos^2x-sin^2 2x+color(red)((4+1))sin^2x=4#.
#:. 4cos^2x-sin^2 2x+4sin^2x+sin^2x=4#.
#:. cancel((4cos^2x+4sin^2x))-sin^2 2x+sin^2x=cancel4#.
#:. sin^2x-sin^2 2x=0#.
But, #sin^2theta-sin^2phi=sin(theta+phi)sin(theta-phi)#.
#:. sin(x+2x)sin(x-2x)=0, i.e., #
# (sin3x)(-sinx)=0..............[because, sin(-x)=-sinx]#,
#:. sin3x=0, or, sinx=0#.
#:. 3x=kpi, or x=kpi, k in ZZ#.
#:. x=kpi/3, or x=kpi, k in ZZ#.
#:. x in {kpi/3}uu{kpi}, k in ZZ#.
But, #because {kpi} sub {kpi/3}, k in ZZ, x in {kpi/3 | k in ZZ}#.
#:. x in [0,2pi] sup {kpi/3 | k in ZZ}#
#={0, pi/3, 2pi/3, pi, 4pi/3, 5pi/3, 2pi}#.