[en] We present a new measurement of the unitarity triangle angle φ₃ using a Dalitz plot analysis of the K_S⁰π⁺π^- decay of the neutral D meson produced in B^±→D⁽*⁾K^± decays. The method exploits the interference between D⁰ and D⁰ to extract the angle φ₃, strong phase δ, and the ratio r of suppressed and allowed amplitudes. We apply this method to a 605 fb^-1 data sample collected by the Belle experiment. The analysis uses three decays: B^±→DK^±, and B^±→D*K^± with D*→Dπ⁰ and D*→Dγ, as well as the corresponding charge-conjugate modes. From a combined maximum likelihood fit to the three modes, we obtain φ₃=78.4 deg. (+10.8 deg./-11.6 deg.)±3.6 deg. (syst)±8.9 deg. (model). CP conservation in this process is ruled out at the confidence level (1-CL)=5x10^-4, or 3.5 standard deviations.