Following similar approaches in the past, the Schrodinger equation for three neutrino propagation in
matter of constant density is solved analytically by two successive diagonalizations of 2x2 matrices.
The final result for the oscillation probabilities is obtained directly in the conventional parametric
form as in the vacuum but with explicit simple modification of two mixing angles ($\theta_{12}$ and $\theta_{13}$) and
mass eigenvalues.