  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.
