Volume formula for a ${\mathbb{Z}}_2$-symmetric spherical tetrahedron through its edge lengths

The present paper considers volume formulae, as well as trigonometric identities, that hold for a tetrahedron in 3-dimensional spherical space of constant sectional curvature +1. The tetrahedron possesses a certain symmetry: namely rotation through angle $\pi$ in the middle points of a certain pair of its skew edges.