  Suppose that $\theta_1,\theta_2,\dots,\theta_n$ are positive numbers and
$n\ge 3$. Does there exist a sphere with a spherical metric with $n$ conical
singularities of angles $2\pi\theta_1,2\pi\theta_2,\dots,2\pi\theta_n$? A
sufficient condition was obtained by Gabriele Mondello and Dmitri Panov
(arXiv:1505.01994). We show that it is also necessary when we assume that
$\theta_1,\theta_2,\dots,\theta_n \not\in \mathbb{N}$.
