We show that precision measurement of (1) sum of neutrino masses by cosmological observation and (2) lifetime of neutrinoless double beta decay in ton-scale experiments, with supplementary use of (3) effective mass measured in single beta decay experiment, would allow us to obtain information on the Majorana phase of neutrinos. To quantify the sensitivity to the phase we use the CP exclusion fraction, a fraction of the CP phase parameter space that can be excluded for a given set of assumed input parameters, a global measure for CP violation. We illustrate the sensitivity under varying assumptions, from modest to optimistic ones, on experimental errors and theoretical uncertainty of nuclear matrix elements. Assuming that the latter can be reduced to a factor of ~1.5 we find that one of the two Majorana phases (denoted as alpha_(21)) can be constrained by excluding ~10-40% of the phase space at 2sigma CL even with the modest choice of experimental error for the lowest neutrino mass of 0.1 eV. The characteristic features of the sensitivity to alpha_(21), such as dependences on the true values of alpha_(21), are addressed.
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