PARISA HAFEZI THE Islamic Republic hanged a man in public who state media said had been convicted of killing two members of the security forces, the second execution in less than a week of people involved in protests against Iran's ruling theocracy. Nationwide unrest erupted three months ago after the death while in detention of 22-year-old Kurdish-Iranian woman Mahsa Amini, who was arrested by morality police enforcing the Islamic Republic's mandatory dress code laws. The demonstrations have turned into a popular revolt by furious Iranians from all layers of society, posing one of the worst legitimacy challenges to the Shi'ite clerical elite…