The computational scheme, termed spin-restricted ensemble-referenced Kohn-Sham (REKS) method (M. Filatov, S. Shaik, Chem. Phys. Lett. 304 (1999) 429; M. Filatov, S. Shaik, J. Phys. Chem. A 104 (2000) 6628), developed earlier to treat the strong non-dynamic correlation in singlet diradicals is extended for doublet states of triradicals. The energy and the density in the REKS method are represented as weighted sums of energies and densities of several KS determinants. The new method, dubbed REKS(3,3), is applied to calculation of several model problems where the conventional spin-unrestricted density functional calculations break the spatial symmetry. The results of the REKS(3,3) calculations show that the method avoids an artificial symmetry breaking in open-shell systems.