A.Math -- trigonometry: [compound angles]

sin^4x + cos^4x = sin 2x
(sin^2x + cos^2x)^2 -2sin^2xcos^2x = sin2x
1-(1/2)sin^2(2x)=sin(2x)
sin^2(2x) + 2sin(2x) -2=0
sin(2x)=-1+√3 or -1-√3 (rej)
2x=180°n+(-1)^n(47.05°)
x=90°n+(-1)^n(23.5°)