${\left[ {\begin{array}{*{20}{c}}
{\vec a}&{\vec b}&{\vec c}
\end{array}} \right]^2} = \left| {\begin{array}{*{20}{c}}
1&{\cos \theta }&{\cos \theta }\\
{\cos \theta }&1&{\cos \theta }\\
{\cos \theta }&{\cos \theta }&1
\end{array}} \right|$
${\left[ {\begin{array}{*{20}{l}}
{\overrightarrow a }&{\overrightarrow b }&{\overrightarrow c }
\end{array}} \right]^2} = {(1 - \cos \theta )^2}(1 + 2\cos \theta ) \ge 0$
${\cos \theta \geq-\frac{1}{2}} $
${\theta=\frac{2 \pi}{3}}$
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