Gwyneth Paltrow has cashed in on her trademark golden tresses. Paltrow got shorn Thursday night at Prive Salon on Melrose Place for her upcoming role in the movie “Sliding Doors.” Owner Laurent Dufourg, who styled her for the Golden Globes, fearlessly cut layers into the hair that used to hang to the middle of Paltrow’s back. “It’s a short cut with bangs,” said Dufourg, “layered to the neck. It’s shorter than a bob. I did a razor cut on her.” So what did her fiance think? “Brad Pitt loved it,” Dufourg reported. “He was here the whole time holding her hand.” Another golden girl, Anna Nicole Smith, watched the spectacle from the next chair.