The verification of the sterile neutrino hypothesis and, if confirmed, the determination of the relevant oscillation parameters is one of the goals of the neutrino physics in near future. We propose to search for the sterile neutrinos with a high statistics measurement utilizing the radioactive sources and oscillometric approach with large liquid scintillator detector like LENA, JUNO, or RENO-50. Our calculations indicate that such an experiment is realistic and could be performed in parallel to the main research plan for JUNO, LENA, or RENO-50. Assuming as the starting point the values of the oscillation parameters indicated by the current global fit (in 3 + 1 scenario) and requiring at least 5σ confidence level, we estimate that we would be able to detect differences in the mass squared differences of electron neutrinos and electron antineutrinos of the order of 1% or larger. That would allow to probe the CPT symmetry with neutrinos with an unprecedented accuracy.