  We present results of timing measurements of the binary millisecond pulsar
PSR J2145-0750. Combining timing data obtained with the Effelsberg and Lovell
radio telescopes we measure a significant timing parallax of 2.0(6) mas placing
the system at 500 pc distance to the solar system. The detected secular change
of the projected semi-major axis of the orbit $\dot x=1.8(6)\times 10^{-14}$
lt-s s$^{-1}$, where $x=(a_{\rm p}\sin i)/c$, is caused by the proper motion of
the system. With this measurement we can constrain the orbital inclination
angle to $i<61\degr$, with a median likelihood value of $46\degr$ which is
consistent with results from polarimetric studies of the pulsar magnetosphere.
This constraint together with the non-detection of Shapiro delay rules out
certain combinations of the companion mass, $m_2$, and the inclination, $i$.
For typical neutron star masses and using optical observations of the
carbon/oxygen-core white dwarf we derive a mass range for the companion of $0.7
M_\odot\leq m_2\leq 1.0 M_\odot$. We apply evolutionary white dwarf cooling
models to revisit the cooling age of the companion. Our analysis reveals that
the companion has an effective temperature of $T_{\rm eff}=5750\pm600$ K and a
cooling age of $\tau_{\rm cool}=3.6(2)$ Gyr, which is roughly a factor of three
lower than the pulsar's characteristic age of 10.4 Gyr. The cooling age implies
an initial spin period of $P_0=13.0(5)$ ms, which is very close to the current
period.
