In the weak field scheme, the complete diagonalizing Hamiltonian matrices and th e constants of crystal structure and g factor of electron paramagnetic resonanc e are derived for 3d4/3d6 ions configuration in the trigon al symmetry in terms of Racahs irreducible tensor operator method. The ground- state energy levels and the constants of crystal structure and g factor of elec tron paramagnetic resonance of the Co3+ in LiCoO2 and LiCo O2:Ni crystals are studied. The spin singlets and triplet of the grou nd-state energy levels of the Co3+ in LiCoO2 and LiCoO2:Ni crystals are taken into consideration in the calculation and applica tion of the crystal-field energy of 3d4/3d6. The changes o f the constants of local structure, which are the causes of the changes of the g round-state energy levels of the Co3+, and the values of g factor of electron paramagnetic resonance of Co3+ in LiCoO2 and LiCo O2:Ni crystals are also studied. The theoretical results are in good agreement with the experimental observations.