a*(a+2b)=(cosa,sina)*[(cosa,sina)+2(cosb,sinb)]
=(cosa,sina)*(cosa+2sinb,sina+2cosb)
=cosa(cosa+2sinb)+sina(sina+2cosb)
=cosa^2+sina^2+2cosacosb+2sinasinb
=1+2cos(a-b)
范围：【-1,3】
a-b=π/3,
|a+2b|^2=(a+2b)^2=|a|^2+4a*b+4|b|^2
=5+4*(cosacosb+sinasinb)
=5+4cos(a-b)=5+4cosπ/3=7
|a+2b|=根号7