What type of government did the romans establish after they overthrew the last etruscan king?

The Overthrow of the Roman monarchy was a political revolution in ancient Rome in around 509 BC, which resulted in the expulsion of the last king of Rome, Lucius Tarquinius Superbus, and the establishment of the Roman Republic.

The Roman histories tell that while the king was away on campaign, his son Sextus Tarquinius raped a noblewoman Lucretia. Afterwards, she revealed the offence to various Roman noblemen, and then committed suicide. The Roman noblemen, led by Lucius Junius Brutus, obtained the support of the Roman aristocracy and the people to expel the king and his family and to institute a republic. The Roman army supported Brutus, and the king went into exile. Despite a number of attempts by Lucius Tarquinius Superbus to reinstate the monarchy, the republic was established and two consuls were elected annually to rule the city.