Which was, to my knowledge, an unconstitutional act. If you have some evidence that suggests that the lower house of Chile's bicameral legislature had the constitutional authority to legitimate a military coup, then by all means, present it.
Honestly, I thought you were one of those "republic not a democracy" people. You'd think someone who understands the meaning of republicanism would understand whether or not the lower house of the chilean legislature had the constitutional authority to call for a military coup.
That doesn't seem to be the case at all. The CoD declaration contained a list of constitutional breaches by Allende presented to the "President of the Republic, Ministers of State, and members of the Armed and Police Forces" to inform them of the "breakdown of the legal and constitutional order of the Republic." The declaration then invoked the constitutional oath taken by those parties to restore the constitution. Allende was given the opportunity to do so, but the same oath also bound the military if he did not. Pinochet's action was dictated by his oath. The point of the CoD declaration was to list the charges and invoke that oath as a basis for arresting Allende should he not come back into compliance with the constitution.
To be unconstitutional, an act must violate something specific in the constitution itself. For example, Allende violated several dozen specific clauses in the Chilean constitution and was found in violation of them by both the Supreme Court and the Legislature.
To my knowledge there was nothing in the constitution actively barring the Chamber of Deputies from asking the police and military to defend the constitution against its attackers. There wasn't a process spelling out step by step how they were to do this, but certainly nothing prohibiting them from doing it, particularly when facing a threat of constitutional overthrow itself.