Another solution. The points are vertices of a regular septagon. It follows from the rotational symmetry of the polygon that: Log in to Reply
![\[\cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7}=\frac{1}{2}\]](https://www.math.tolaso.com.gr/wp-content/ql-cache/quicklatex.com-587a71ae161fe6739695d5a317989abc_l3.svg "Rendered by QuickLaTeX.com")
. Its eigenvalues are 
. Hence,![\[\Tr\left ( A \right ) = 1 = 2 \left ( \cos \frac{\pi}{7} + \cos \frac{3\pi}{7} + \cos \frac{5\pi}{7} \right )\]](https://www.math.tolaso.com.gr/wp-content/ql-cache/quicklatex.com-8eb8db7e0ef528460182192786d805fa_l3.svg "Rendered by QuickLaTeX.com")
Another solution.
The points
are vertices of a regular septagon. It follows from the rotational symmetry of the polygon that: