After he took the stand in court last week to explain the events that led to his fatal shooting of a 27-year-old father of three during a traffic stop gone wrong, Chicago cop Raoul Mosqueda was quickly forced to admit that a critical part of his story was wrong.

But that embarrassing revelation seemed to have little effect on a federal jury, which on Wednesday cleared Mosqueda and his partner, Gildardo Sierra, of any wrongdoing in the death of Darius Pinex anyway.

The verdict clearing Mosqueda, Sierra and the City of Chicago of any civil liability in Pinex’s death on Jan. 7, 2011, left Pinex’s family, which had asked for $10 million in compensation, in shock.

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“They’ve been lying to me for four whole years,” Pinex’s mother, Gloria Pinex, said through tears in the lobby of the Dirksen Federal Building after the verdict was announced.

“Justice for Darius Pinex and the other mothers who have lost their sons to Chicago Police officers!”

A jury of four white men, two black men and two white women deliberated for a total of about seven hours at the end of a weeklong trial before delivering their verdict in favor of the officers in the wrongful-death and excessive force case.

The Pinex family’s hopes of victory had seemed to increase dramatically last week when lawyers for the city finally handed over to the Pinex family’s lawyers a long-missing recording of a police radio call that directly contradicted Mosqueda’s sworn testimony of the events leading up to Pinex’s death.

Mosqueda had long argued that he and Sierra pulled over Pinex’s Oldsmobile at the corner of Marquette and Racine because it matched the description given over the police radio of a car used in a shooting earlier that night — an account he repeated on the stand last week, telling jurors the description on the radio described a green car with aftermarket rims, just like Pinex’s.

But the recording of the radio transmission showed that the dispatcher made no reference to the car’s color, wheels — or any shooting or possible armed occupants.

Representing the Pinex family, attorney Steve Greenberg said the tape proved Mosqueda was a “liar.”

And an angry U.S. District Judge Edmond Chang last week chastised the city for failing to turn over the tape sooner. In the coming weeks, he could yet sanction the city or order a retrial.

Lawyers for the city said that Mosqueda and Sierra opened fire because they were in fear of their lives when Pinex tried to escape by backing up, then driving forward toward them after he had been pulled over.

Pinex tried to flee because he was drunk and had a gun hidden under his seat, they alleged, pointing to large discrepancies in the changing accounts of Pinex’s pal, Matthew Colyer, who was riding in Pinex’s car and joined in the lawsuit against the officers.

Buy Pinex and Colyer’s lawyers say that Pinex threw his car into reverse only after the cops started shooting, and that he never posed a threat to the officers.

Both Mosqueda and Sierra declined to comment as they left court.

Sierra was involved in two other shootings in the six months after Pinex’s death.

The city previously paid $4.1 million to the family of Flint Farmer, whom Sierra fatally shot in the back after mistaking his cellphone for a gun.