If origin is the orthocentre of a triangle formed by the points $(\cos \alpha ,\sin \alpha ,0)$ , $(\cos \beta ,\sin \beta ,0)$ , $(\cos \gamma ,\sin \gamma ,0)$  then ${\displaystyle \sum \cos (2\alpha -\beta -\gamma )=}$

$OA=\sqrt{{\cos }^2\alpha +{\sin }^2\alpha }=1$ = OB = OC

            $\Rightarrow \Delta$ ABC is an equilateral ${\Delta }^{\ell e}$ .

            $\Rightarrow \cos \alpha +\cos \beta +\cos \gamma =\sin \alpha +\sin \beta +\sin \gamma =0$                                                      

            $\Rightarrow \Sigma \cos \left(2\alpha -\beta -\gamma \right)=3$