A theoretical framework is presented for analysis of all three "multiline" EPR spectra (MLS) arising from the tetramanganese (Mn-4) cluster in the S-2 oxidation state of the photosynthetic water oxidizing complex (WOC). Accurate simulations are presented which include anisotropy of the g and (four) Mn-55 hyperfine tensors, chosen according to a database of Mn-55(III) and Mn-55(IV) hyperfine tensors obtained previously using unbiased least-squares spectral fitting routines. In view of the large (30%) anisotropy common to Mn(III) hyperfine tensors in all complexes, previous MLS simulations which have assumed isotropic hyperfine constants have required physically unrealistic parameters. A simple model is found which offers good simulations of both the native "19-21-line" MLS and the "26-line" NH3-bound form of the MLS. Both a dimer-of-dimers and distorted-trigonal magnetic models are examined to describe the symmetry of the Heisenberg exchange interactions within the Mn-4 cluster and thus define the initial electronic basis states of the cluster.