$\Leftrightarrow 4sin^4x+4sin^4(x+\pi/4)+4sin^4(x-\pi/4)=9/2$$\Leftrightarrow (1-cos2x)^2+(sinx+cosx)^4+(sinx-cosx)^4-9/2=0$
$\Leftrightarrow 1-2cos2x+cos^22x+(1+sin2x)^2+(1-sin2x)^2-9/2=0$
$\Leftrightarrow 3-2cos2x+2sin^22x-9/2=0$
$\Leftrightarrow 5-9/2-2cos2x-2cos^22x=0$
$\Leftrightarrow 2cos^22x+2cos2x-1/2=0$ coi như xong