2sin(pi/4+x)sin(pi/4+x)+sin^2x=0

sin(π/2+2x)+sin^2x=0;
cos^2(2x)+sin^2x=0;
cos^2x-sin^2x+sin^2x=0;
cos^2x=0;
cosx=0;
x=π/2+πn,n∈Z