A detailed multifrequency high-field-high-frequency EPR (95-285 GHz) study has been performed on the single-molecule magnet of formula [Fe8O2(OH)12(tacn)6]Br8 x 9H2O, in which tacn = 1,4,7-triazacyclononane. Polycrystalline powder spectra have allowed the estimation of the zero-field splitting parameters up to fourth order terms. The single-crystal spectra have provided the principal directions of the magnetic anisotropy of the cluster. These results have been compared with an evaluation of the intra-cluster dipolar contribution to the magnetic anisotropy; this suggests that single-ion anisotropy is the main contributor to the magnetic anisotropy. The role of the transverse magnetic anisotropy in determining the height of the barrier for the reversal of the magnetization is also discussed.