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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   $2\pi \vartheta _1,\ldots ,2\pi \vartheta _n$   and non-coaxial holonomy. Such a necessary and sufficient condition is expressed in terms of linear inequalities in   $\vartheta _1,\ldots ,\vartheta _n$  .

Spherical Metrics with Conical Singularities on a 2-Sphere: Angle Constraints