The bright Kreutz Comet C/2007 L3 (SOHO) entered the fields of view of the twin Solar Terrestrial Relations Observatory (STEREO) COR1 telescopes on 7-8 June 2007. The 12 β’ separation between the two spacecraft at the time afforded the opportunity to derive the position of the comet's tail in three-dimensional space using direct triangulation. The track of the comet's orbit is compared against more traditional orbital calculations using observations from the STEREO COR2 telescopes, and from the Large Angle and Spectrometric Coronagraph (LASCO) aboard the Solar and Heliospheric Observatory (SOHO). The shape of the comet's tail shows that it is composed of dust particles released when the comet was between 18 and 22 solar radii, with no significant dust production after that. The comet did not survive perihelion passage, but a rare faint remnant of the comet tail persisted for several hours after the break-up, and was seen by both the SOHO and STEREO coronagraphs to drift slowly away from the Sun. This tail remnant was found to be composed of particles far back from the head of the comet. The motion of the tail remnant shows a loss of angular momentum during the passage through the solar corona. Atmospheric drag is estimated to account for a significant fraction of this change in angular momentum, but indications are that other mechanisms may be required to completely account for the total amount of change.