因为 (sinθ)^4-(cosθ)^4=5/9,
所以 [(sinθ)^2+(cosθ)^2][(sinθ)^2-(cosθ)^2]=5/9,
即 (sinθ)^2-(cosθ)^2=5/9.
所以 cos2θ=(cosθ)^2-(sinθ)^2=-5/9.
所以 cos4θ =cos2(2θ)=2( cos2θ )^2-1
=2*(-5/9)^2-1=-31/81.