sin(π/4+a)*sin(π/4-a)=1/6,sin(π/4+a)*sin(π/2-(π/4+a))=1/6,sin(π/4+a)*cos(π/4+a) =1/6,1/2 sin(π/2+2a) =1/6,sin(π/2+2a) =1/3,cos2a =1/3.∵a∈（π/2,π),2a∈（π,2π),∴sin2a