sin(π/4+x)sin(π/4-x)=sin(π/4+x)cos(π/4+x)=sin(π/2+2x)/2=cos2x/2=1/6
∵x(π/2,π),∴2x(π,2π)
∴sin2x<0
∴sin2x=-2√2/3
∴sin4x=2sin2xcos2x=-4√2/9.