To free Haken in Stay of Execution in the Hidden City in Shadow of the Tomb Raider talk to the musician in the square to lure away the guards.
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Talk to the musician to lure away the guards to free Haken in Stay of Execution in the Hidden City in Shadow of the Tomb Raider
Talk to the guy squatting to the left of the prison to get him to help you open the door.

Talk to the guy squatting to the right of the prison door to get him to help you open the prison door to free Haken in Stay of Execution in the Hidden City in Shadow of the Tomb Raider
Then talk to the guy standing to the right of the prison to help the other guy.

Talk to the guy standing to the left of the prison door to get him to help you open the prison door to free Haken in Stay of Execution in the Hidden City in Shadow of the Tomb Raider
Walk up to the prison door and lead Haken out of his prison.