A coup is a change in leadership enacted outside of the accepted legal method for that unit of governance it has nothing to do with leaving the patent unit.
Perhaps that was insufficiently clear. Every nation has an acceptable legal method for choosing new leadership
> A coup d'état, or simply a coup, is an illegal and overt attempt by the military or other government elites to unseat the incumbent leader by force. A self-coup is when a leader, having come to power through legal means, tries to stay in power through illegal means.
The proper turn when an existing power structure attempts to detach itself from its superiors is secession