1/4sin2a．sin2a+sinb.sinb+cosa.cosa.cosa.cosa
=sina^2*cosa^2+sinb^2+cosa^2*cosa^2
=cosa^2(sina^2+cosa^2)+sinb^2
=cosa^2+sinb^2
sin(a+b)sin(a-b)=1/3
(sinacosb+cosasinb)(sinacosb-cosasinb)=1/3
sina^2cosb^2-cosa^2sinb^2=1/3
(1-cosa^2)(1-sinb^2)-cosa^2sinb^2=1/3
[1+cosa^2sinb^2-(cosa^2+sinb^2)]-cosa^2sinb^2=1/3
1-(cosa^2+sinb^2)=1/3
cosa^2+sinb^2=2/3
所以1/4sin2a．sin2a+sinb.sinb+cosa.cosa.cosa.cosa=2/3