a/sinA=b/sinB=c/sinC
(a+c)/(sinA+sinC)=b/sinB
sinB/(sinA+sinC)=b/(a+c)=(a-c)/(b-c)
b(b-c)=(a+c)(a-c)
b^2-bc=a^2-c^2
b^2+c^2-a^2=bc
(b^2+c^2-a^2)/bc=1
cosA=(b^2+c^2-a^2)/2bc=1/2
A=60°