  A spherical quadrilateral is a bordered surface homeomorphic to a closed
disk, with four distinguished boundary points called corners, equipped with a
Riemannian metric of constant curvature 1, except at the corners, and such that
the boundary arcs between the corners are geodesic. We discuss the problem of
classification of these quadrilaterals and perform the classification up to
isometry in the case that two angles at the corners are multiples of pi. The
problem is equivalent to classification of Heun's equations with real
parameters and unitary monodromy.
