  We further develop a simple and compact technique for calculating the three
flavor neutrino oscillation probabilities in uniform matter density. By
performing additional rotations instead of implementing a perturbative
expansion we significantly decrease the scale of the perturbing Hamiltonian and
therefore improve the accuracy of zeroth order. We explore the relationship
between implementing additional rotations and that of performing a perturbative
expansion. Based on our analysis, independent of the size of the matter
potential, we find that the first order perturbation expansion can be replaced
by two additional rotations and a second order perturbative expansion can be
replaced by one more rotation. Numerical tests have been applied and all the
exceptional features of our analysis have been verified.
