Observation of Direct<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>Violation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>B</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo>→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>Decays and Model-Independent Constraints on the Quark-Mixing Angle<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>ϕ</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

We report a new measurement of the time-dependent CP-violating parameters in B(0)-->pi(+)pi(-) decays with 535 x 10(6) BB pairs collected with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider operating at the Upsilon(4S) resonance. We find 1464+/-65 B(0)-->pi(+)pi(-) events and measure the CP-violating parameters S(pipi)=-0.61+/-0.10(stat)+/-0.04(syst) and A(pipi)=+0.55+/-0.08(stat)+/-0.05(syst). We observe large direct CP violation with a significance greater than 5 standard deviations for any S(pipi) value. Using isospin relations, we measure the Cabibbo-Kobayashi-Maskawa quark-mixing matrix angle phi(2)=(97+/-11) degrees for the solution consistent with the standard model and exclude the range 11 degrees <phi(2)<79 degrees at the 95% confidence level.