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 $i<61degr$, with a median likelihood value of $46degr$ 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 $0.7 M_odotleq m_2leq 1.0 M_odot$. 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 $T_{rm eff}=5750pm600$ K and a cooling age of $tau_{rm cool}=3.6(2)$ Gyr, which is roughly a factor of three lower than the pulsars 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.
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