sin²B=sin²（A+C)=（sinAcosC+sinCcosA）²=sin²Acos²C+sin²Ccos²A+2sinAcosCsinCcosA
∴sin²A+sin²C+sinA.sinC=sin²Acos²C+sin²Ccos²A+2sinAcosCsinCcosA
整理得2sin²Asn²C+sinAsinC=2sinAcosCsinCcosA
sinAsinC(1+2sinAsinC)=2sinAsinCcosAcosC
1+2sinAsinC=2cosAcosC
cos(A+C)=1/2
π-B=π/3 B=2π/3 sinB=√3/2
1/2acsinB=2√3 ac=8
∴a=4 c=2 或a=2 c=4