The LHCb experiment (CERN) will offer a precise hadronic probe with which to study CP violation, rare decays and possible New Physics (NP) effects occurring in the b-system. Contained within the vast physics program is a dedicated and intense effort to measure the CP violating weak mixing phase, βs. This phase, observable in the neutral Bs-system, presents a sensitive indicator to NP occurring at the TeV scale. This phase appearing through the theoretically clean ¯b → ¯cc¯s quarklevel transition, can be measured precisely using Bs → J/ψφ decays. The analysis of Bs → J/ψφ decays requires using its decay angular information to separate out the CP eigenstates. The sensitivity to βs can then be extracted from the angular differential rates for this mode. This thesis presents the selection and reconstruction of this decay channel, analysis of the background specific to this channel and the method for fitting the data to extract βs. Previous studies within the collaboration have shown the βs sensitivity using a reduced angular expression for the decay rates. By studying the full angular expression, we find both a quantitative and qualitative improvement in the precision with which βs is obtained: the precision improves by approximately 20%, from ± 0.027 to ± 0.022 radians. In addition, we find it is possible to extract the b-tagging parameter from data itself, which aids to minimise the overall systematic effect. This thesis, in preparation for data taking at the LHCb, presents this expected improvement in measuring βs.