We report a new measurement of the time-dependent CP-violating parameters in B0→π+π- decays with 535×106 BB̄ pairs collected with the Belle detector at the KEKB asymmetric-energy e+e- collider operating at the Υ(4S) resonance. We find 1464±65 B0→π+π- events and measure the CP-violating parameters Sππ=-0.61±0.10(stat)±0. 04(syst) and Aππ=+0.55±0.08(stat)±0.05(syst). We observe large direct CP violation with a significance greater than 5 standard deviations for any Sππ value. Using isospin relations, we measure the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle 2=(97±11)° for the solution consistent with the standard model and exclude the range 11°< 2<79° at the 95% confidence level. © 2007 The American Physical Society.