  Following the semiclassical formalism of Strutinsky et al., we have obtained
the complete eigenvalue spectrum for a particle enclosed in an infinitely high
spheroidal cavity. Our spheroidal trace formula also reproduces the results of
a spherical billiard in the limit $\eta\to1.0$. Inclusion of repetition of each
family of the orbits with reference to the largest one significantly improves
the eigenvalues of sphere and an exact comparison with the quantum mechanical
results is observed upto the second decimal place for $kR_{0}\geq{7}$. The
contributions of the equatorial, the planar (in the axis of symmetry plane) and
the non-planar(3-Dimensional) orbits are obtained from the same trace formula
by using the appropriate conditions. The resulting eigenvalues compare very
well with the quantum mechanical eigenvalues at normal deformation. It is
interesting that the partial sum of equatorial orbits leads to eigenvalues with
maximum angular momentum projection, while the summing of planar orbits leads
to eigenvalues with $L_z=0$ except for L=1. The remaining quantum mechanical
eigenvalues are observed to arise from the 3-dimensional(3D) orbits. Very few
spurious eigenvalues arise in these partial sums. This result establishes the
important role of 3D orbits even at normal deformations.
