Verified answer

sin(60+2a)sin(60-2a)=1/2(cos4a-cos120)=1/2cos4a-1/2cos(90+30)=

=1/2cos4a+1/4=1/2(cos4a+1/2)

2/sin2a(cos4a+1/2)=4/sin2a(2cos4a+1)=4/sin2a(2-4sin^2(2a)+1)=

=4/(3sin2a-4sin^3(2a))=4/sin6a