If $a, b, c\in \mathbb{C}$, and if $\left \| a \right \|=\left \| b \right \|=\left \| c \right \|=1$, prove $(a+b)(b+c)(c+a)/(abc)\in \mathbb{R}$.
I have thought this Q for a long time, but I can only get something long and troublesome but not the answer. Can anyone help me please? THANK YOU! ~