由余弦定理得：
cosC=(a²+b²-c²)/2ab=(4+9-16)/12=-1/4
cos²C=1/16
sin²C=1-cos²C=1-1/16=15/16
sinC=√15/4
cos2C=cos²C-sin²C=1/16-15/16=-7/8
sin2C=2sinCcosC=2×√15/4×(-1/4)=-√15/8
cos(2c+π/3)
=cos2Ccosπ/3-sin2Csinπ/3
=-7/8×1/2-(-√15/8)×√3/2
=-7/16+3√5/16
=(3√5-7)/16