sin^6 a+cos^6 a+3sin^2 acos^2a=(sin^2 a+cos^2 a)(sin^4 a+cos^4 a-sin^2 acos^2 a)+3sin^2 acos^2a=sin^4 a+cos^4 a-sin^2 acos^2 a+3sin^2 acos^2a=sin^4 a+cos^4 a+2sin^2 acos^2 a=(sin^2 a+cos^2 a)^2=1