真ん中の辺の長さをa

a-d=2sinC
a=2sin(180-3C)=2sin(3C)=2(3sinC-4(sinC)^3)=2sinC(3-4(sinC)^2)…(ii)
a+d=2sin(2C)=4sinCcosC

2a=2sinC+4sinCcosC=2sinC(1+2cosC)
a=sinC(1+2cosC)…(i)

(i)=(ii)
sinC(1+2cosC)=2sinC(3-4(sinC)^2)
1+2cosC=2(3-4(sinC)^2)=2(3-4(1-(cosC)^2))=2(-1+4(cosC)^2)
8(cosC)^2-2cosC-3=0
(4cosC-3)(2cosC+1)=0