if $\alpha ,\beta ,\gamma$ are real numbers then without expending at any stage. Show that $\left|\begin{array}{ccccc}1& & \cos \left(\beta -\alpha \right)& & \cos \left(\gamma -\alpha \right)\\ \cos \left(\alpha +\beta \right)& & 1& & \cos \left(\gamma -\beta \right)\\ \cos \left(\alpha -\gamma \right)& & \cos \left(\beta -\gamma \right)& & 1\end{array}\right|=0$

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