Under what conditions, is it legitimate to use violence to achieve political goals? In a revolution, is the execution of the king necessary or wise?

It is always better to use diplomacy to solve issues but often times violence is necessary. When someone feels so strongly about their ideas or thoughts that they are willing to die for them that is when violence is necessary, that is if you are threatened by them. Just because someone disagrees with you does not mean you should kill them but if it needed due to self preservation then violence becomes a tool. Think of all the people who claim they would accept death rather than change their lives. New Hampshire's state motto is Live Free or Die. Insurgents and terrorists also accept death. When your country's safety is threatened by someone who would die before listening to your diplomats or considering a compromise then the only solution is to remove your opponent from existence.
Killing a king or leader is a symbol. That leader was a symbol of old times, of what the rebels want to change, and as long as that symbol lives there will be those who want to follow that leader for their own gains. The death of a leader symbolizes the end of current policies and problems.