Our concern is the spin sublevels of the first excited triplet state of a d(6) electron system in a cubic field. To that end, we will construct exact analytic eigenvalues and eigenfunctions for these sublevels. The essential point is that we formulate the total wave functions, space plus spin, so that they form bases for the irreducible representations of the O' double group. By virtue of such a choice, the matrix with respect to the total Hamiltonian, which comprises both crystal field potential and spin-orbit coupling, is a priori diagonalized for any triplet manifold. That is, the symmetry-adapted wave functions are eigenfunctions of the total Hamiltonian. Configuration interaction among the sublevels of different triplet states may also be expressed analytically, and the resulting eigenvalues and eigenfunctions may be obtained as a function of the spin-orbit coupling parameter zetand and the T-3(1)-T-3(2) energy gap, DeltaE (i.e., 8B, where B is the Racah parameter). The sublevel energies obtained in this way are compared with the energies of the lowest three emitting levels observed for K3Co(CN)(6). From the experimental energy separations, zeta(3d) and B are obtained as 576 and 500 cm(-1), respectively. Since these are reasonable values, we conclude that the experimentally identified emitting states are indeed the spin sublevels of the lowest triplet state, T-3(1).