(1+tan²2a)[cos(2a+π/3)+coa(2a-π/3)](1+tan²2a)[cos(2a+π/3)+cos(2a-π/3)]

(1+tan²2a)[cos(2a+π/3)+coa(2a-π/3)](1+tan²2a)[cos(2a+π/3)+cos(2a-π/3)]
(1+tan²2a)[cos(2a+π/3)+coa(2a-π/3)]
(1+tan²2a)[cos(2a+π/3)+cos(2a-π/3)]

(1+tan²2a)[cos(2a+π/3)+coa(2a-π/3)](1+tan²2a)[cos(2a+π/3)+cos(2a-π/3)]
原式=(sin²2a+cos²2a)/cos²2a*[2cos2acosπ/3]=1/cos²2a*cos2a=1/cos2a

参考例题：
化简 coa^ 2a+cos^2 (a+π/3)-cosa cos(a+π/3)
coa^ 2a+cos^2 (a+π/3)-cosa cos(a+π/3)
=(cosa)^2-cos(π/3+a)[cosa-cos(π/3+a)]
=(cosa)^2-cos(π/3+a)sin(π/6+a)
=(cosa)^2-1/2*[sin(2a+π/2)-1/2]
=(cosa)^2-1/2*cos2a+1/4
=(cosa)^2-1/2*[2(cosa)^2-1]+1/4
=3/4.