Trigonometric Equations

$\cos (\alpha+\beta)+\cos (\beta+\gamma)+\cos (\gamma+\alpha)$

$\cos ^2 \alpha+\cos ^2 \beta+\cos ^2 \gamma$

$\sin ^2 \alpha+\sin ^2 \beta+\sin ^2 \gamma$

$\cos (2 \alpha-\beta-\gamma)+\cos (2 \beta-\gamma-\alpha)+\cos (2 \gamma-\alpha-\beta)$