After several hours of going back and forth on draft night last month, Nets general manager Billy King and his counterpart with the Celtics, Danny Ainge, had come to an agreement on a blockbuster trade to send Paul Pierce, Kevin Garnett and Jason Terry from Boston to Brooklyn. That left one thing to be determined: Whether Garnett would waive his no-trade clause and make the move a reality. So, why, ultimately, did Garnett chose to leave Boston for Brooklyn? “Being able to build something,” he said after yesterday’s press conference introducing the three newest Nets. “The bones of this, to be able to play with Deron Williams and Brook Lopez, Joe Johnson. ... I feel like this was one of the better opportunities I’ve had since I’ve been in the league.” But for Garnett, who is famously loyal, it took some convincing to get him to come around to the idea. Both Williams and coach Jason Kidd put in recruiting calls to Garnett on draft night, but the most persuasive argument may have come from Pierce. “I talked to Jason Kidd, and he was warming me to the [possibility] of coming to Brooklyn,” Pierce said. “Then he started warming me to the fact that they were trying to get Kevin, too. That’s when I called Kevin and asked what he thought about coming to Brooklyn.