Overthrown of a government that the people do not want is something completely democratic thing. It is what the French did in the revolution, it is what the Cubans did, it is what the Nicaraguans did, it is what a lot of nations did. Simply because a coup is supported by the military does not mean it is not legitimate. Military have shifted to right wing politics mostly in the West but it didn't used to be like that and there are multiple examples of this throughout history. Voting isn't the only way to do democracy.