We consider a model of living semiflexible polymers in a solution and obtain results for the liquid-liquid phase separation, which has been a subject of growing interest in the literature and has been studied in some recent experiments. The tetrahedral lattice model is solved exactly on a Husimi cactus of coordination number q=4. The exact solution on the Husimi cactus forms the approximate theory for the original lattice. We consider the end groups to be a different species from the middle groups. This allows us to incorporate the end-group effects in our calculations, which become important at low molecular weights. We investigate the effect of chain rigidity, end-group/middle-group interactions, solvent quality, and the chemical potential of the end-group on the liquid-liquid coexistence curve. We also calculate the average molecular weights of the coexisting liquid phases. The bending penalty epsilon is found to shift the phase diagram only slightly. Attractive end-group/middle-group interaction enhances the phase separation. Due to the exactness of our calculations, the theory never violates thermodynamics and is applicable in the entire parameter space. Our theory also improves upon the classical theories and hence our results should prove useful. (C) 2003 American Institute of Physics.