[1-cos^4(A)-sin^4(A)]/[1-cos^6(A)-sin^6(A)]
=[1-cos^4 A-sin^4 A-2cos^2 A*sin^2 A+2cos^2 A*sin^2 A]/[1-(cos^2 A+sin^2 A)(cos^4 A-cos^2 A*sin^2 A+sin^4 A)]
=[1+2cos^2 A*sin^2 A-（cos^2 A+sin^2 A)]/[1-(cos^4 A-cos^2 A*sin^2 A+sin^4 A)]
=[1+2cos^2 A*sin^2 A-1]/[1-(cos^4 A+2cos^2 A*sin^2 A+sin^4 A)+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/[1-(cos^2 A+sin^2)^2+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/[1-1+3cos^2 A*sin^2 A]
=[2cos^2 A*sin^2 A]/(3cos^2 A*sin^2 A)
=2/3