In this paper a stepwise compaction process of a ring semi-stiff polymer chain placed in a 3d conical nano-cavity and being under the action of the increasing external field is studied. Compaction from a circlelike shape to several toroidal-like loops for a three-dimensional system was observed. The thermodynamic stability of these toroidal-like structures was investigated by observing a hysteresis of the compactionextension curves. This study extends our previous work [1] with investigation of the effect of the cone opening angle variation on the distinct shape transitions.