The City Council voted unanimously Wednesday to approve the payout to the woman, who is one of four women to accuse officers James Nichols and Luis Valenzuela of coercing them into having sex with them, according to court documents. The Times generally does not name alleged sex crime victims.

Nichols and Valenzuela, both 41, were working as narcotics detectives in Hollywood in 2010 when they arrested the woman, according to one of her attorneys, Dennis Chang, and a search warrant affidavit LAPD investigators filed as part of a criminal investigation into the officers’ conduct.

The officers offered to help free the woman from custody as she awaited trial and win her a lenient sentence if she agreed in exchange to work for them as an informant on other investigations, according to Chang and the affidavit.

“Their power over her was abundantly clear from the get go,” Chang said.

Over the next year, Nichols and Valenzuela confronted the woman repeatedly, telling her they would no longer help her in her case unless she had sex with them, Chang and the affidavit said. She agreed, she told investigators, out of fear the officers would send her back to jail if she refused.

In March 2010, Valenzuela showed up at the woman’s apartment while he was off duty and, several months later, had sex with her in…