  We test the cosmological implications of studying galaxy clustering using a
tomographic approach, by computing the galaxy two-point angular correlation
function $\omega(\theta)$ in thin redshift shells using a
spectroscopic-redshift galaxy survey. The advantages of this procedure are that
it is not necessary to assume a fiducial cosmology in order to convert measured
angular positions and redshifts into distances, and that it gives several (less
accurate) measurements of the angular diameter distance $D_\rm{A}(z)$ instead
of only one (more precise) measurement of the effective average distance
$D_\rm{V}(z)$, which results in better constraints on the expansion history of
the Universe. We test our model for $\omega(\theta)$ and its covariance matrix
against a set of mock galaxy catalogues and show that this technique is able to
extract unbiased cosmological constraints. Also, assuming the best-fit
$\Lambda$CDM cosmology from the cosmic microwave background measurements from
the Planck satellite, we forecast the result of applying this tomographic
approach to the final Baryon Oscillation Spectroscopic Survey catalogue in
combination with Planck for three flat cosmological models, and compare them
with the expected results of the isotropic baryon acoustic oscillation (BAO)
measurements post-reconstruction on the same galaxy catalogue combined with
Planck. While BAOs are more accurate for constraining cosmological parameters
for the standard $\Lambda$CDM model, the tomographic technique gives better
results when we allow the dark energy equation of state $w_{DE}$ to deviate
from $-1$, resulting in a performance similar to BAOs in the case of a constant
value of $w_{DE}$, and a moderate improvement in the case of a time-dependent
value of $w_{DE}$, increasing the value of the Figure-of-Merit in the $w_0-w_a$
plane up to $15\%$.
