  In this article we give a criterion for the existence of a metric of
curvature $1$ on a $2$-sphere with $n$ conical singularities of prescribed
angles $2\pi\vartheta_1,\dots,2\pi\vartheta_n$ and non-coaxial holonomy. Such a
necessary and sufficient condition is expressed in terms of linear inequalities
in $\vartheta_1,\dots,\vartheta_n$.
