  The development of the first X-ray polarimeter, based on the photoelectric
effect 20 years ago and implemented thanks to advances in gas amplification
structures and readout techniques, had a significant impact in opening a new
window for X-ray polarimetry. This system measures the X-ray polarization by
reconstructing the initial direction of the photoelectron, emitted by the
interaction of an incident photon with an atomic electron, in a gas mixture
from an ionization track collected on a two-dimensional plane. However, actual
X-ray polarimeters, are still requiring relatively long exposure time and
cannot coupled with high effective area mirrors or concentrators. In this
context, the high yield polarimetry experiment in X-rays (Hype-X) project is
currently underway, aiming to improve the sensitivity of the next generation
X-ray polarimetry detectors taking advantage of the recent advancements in
imaging techniques for high-resolution time projection chambers. In particular,
we are evaluating the use of TIMEPIX3 to be applied for the read-out of a gas
detector, which will allow us to obtain a three-dimensional image of the
photoelectron track. To evaluate the improvement achievable by using a 3D track
reconstruction, in this paper, we have reproduced a three-dimensional
photoelectron track from a 'Geant4' Monte Carlo simulation and examined the
sensitivity of X-ray polarimetry using a new three-dimensional track
reconstruction algorithm. We report the improvement of the modulation factor
with three-dimensional track reconstruction as $\sim5\%$ (relative) in the 2-8
keV range and $\sim17\%$ (relative) in the 2-4 keV range compared to the
current two-dimensional polarimetry system. This is equivalent to add a further
telescope to the three-telescope systems now employed in space on board the
IXPE mission.
