We apply the law of cosines to each of three isosceles triangles
in Figure 9 having a vertex at the center of the heptagon,
two edges of length R and base of length rk, where k = 1,
2, 3. The corresponding vertex angles are θk, where θ1 = 2π/7,
θ2 = 4π/7, θ3 = 6π/7. The law of cosines for the isosceles
triangle with vertex angle θk states that