3sin^2 (2x) + sin2x = (sinx-cosx) ^2

3sin²2x+sin2x=sin²x-2sinxcosx+cos²x

3sin²2x+sin2x=1-sin2x

3sin²2x+sin2x-1+sin2x=0

3sin²2x+2sin2x-1=0

sin2x=a

3a²+2a-1=0

D=4+12=16

a1 = (-2-4) / 6=-1⇒sin2x=-1⇒2x=-π/2+2πn⇒x=-π/4+πn

a2 = (-2+4) / 6=1/3⇒sin2x=1/3⇒2x = (-1) ^n*arcsin1/3+πn⇒x = (-1) ^n*1/2arcsin1/3+πn/2