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$\newcommand{\S}{\mathbb{S}^1}$ $\newcommand{\la}{\lambda}$Let$$M=\{(x_1,x_2,x_3,x_4) \in (\S)^4\,\, |\,\, \text{ all the } x_i \, \text{ are distinct}\} $$ Define $E:M \to \mathbb{R}$ by $$E(x_1,x_2,...