2sin^3x+sinx+2√2(1-cos^2x)=0

2sin^3x+2√2sin^2x+sinx=0

sinx(2sin^2x+2√2sinx+1)=0

sinx=0; x1=pin

2sin^2x+2√2sinx+1=0

D=8-8-0

sinx=-2√2/4=-√2/2; x2=-pi/4+2pik; x3=-3pi/4+2pik; k;n∈Z