$\text{If }\mathrm{\alpha }+\mathrm{\beta }+\mathrm{\gamma }=2\mathrm{\theta }\text{, then }\cos \mathrm{\theta }+\cos (\mathrm{\theta }-\mathrm{\alpha })+\cos (\mathrm{\theta }-\mathrm{\beta })+\cos (\mathrm{\theta }-\mathrm{\gamma })=$

$\begin{array}{l}\cos \mathrm{\theta }+\cos (\mathrm{\theta }-\mathrm{\alpha })+\cos (\mathrm{\theta }-\mathrm{\beta })+\cos (\mathrm{\theta }-\mathrm{\gamma })=2\cos \left(\frac{2\mathrm{\theta }-\mathrm{\alpha }}{2}\right)\cos \left(\frac{\mathrm{\alpha }}{2}\right)+2\cos \left(\frac{2\mathrm{\theta }-\mathrm{\beta }-\mathrm{\gamma }}{2}\right)\cos \frac{\mathrm{\beta }-\mathrm{\gamma }}{2}\\ =2\cos \left(\frac{\mathrm{\beta }+\mathrm{\gamma }}{2}\right)\cos \left(\frac{\mathrm{\alpha }}{2}\right)+2\cos \frac{\mathrm{\alpha }}{2}\cos \frac{\mathrm{\beta }-\mathrm{\gamma }}{2}=2\cos \frac{\mathrm{\alpha }}{2}\left[\cos \frac{\mathrm{\beta }+\mathrm{\gamma }}{2}+\cos \frac{\mathrm{\beta }-\mathrm{\gamma }}{2}\right]=4\cos \frac{\mathrm{\alpha }}{2}\cos \frac{\mathrm{\beta }}{2}\cos \frac{\mathrm{\gamma }}{2}\end{array}$