[en] We exploit the quantum coherence between pair-produced D⁰ and D⁰ in ψ(3770) decays to study charm mixing, which is characterized by the parameters x and y, and to make a first determination of the relative strong phase δ between D⁰→K⁺π^- and D⁰→K⁺π^-. Using 281 pb^-1 of e⁺e^- collision data collected with the CLEO-c detector at E_cm=3.77 GeV, as well as branching fraction input and time-integrated measurements of R_M≡(x²+y²)/2 and R_WS≡Γ(D⁰→K⁺π^-)/Γ(D⁰→K⁺π^-) from other experiments, we find cosδ=1.03_-0.17^+0.31±0.06, where the uncertainties are statistical and systematic, respectively. By further including other mixing parameter measurements, we obtain an alternate measurement of cosδ=1.10±0.35±0.07, as well as xsinδ=(4.4_-1.8^+2.7±2.9)x10^-3 and δ=(22_-12-11⁺¹¹⁺⁹) deg