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Flavour-tagged, time-dependent, angular analysis of the decay $B^0_s \toJ/\psi \phi$ allows the determination of a CP-violating phase which in theStandard Model is denoted $-2\beta_s$, and is predicted to be very small. Manymodels of new physics lead to significant enhancements in the value of thisobservable. LHCb has the capability to improve significantly the existingexperimental knowledge on this phase with the data expected in the 2010 run,and to probe down to the Standard Model prediction within a few years ofoperation. The steps in this measurement programme will be presented.Discussion will also be given to other methods to determine this phase, andrelated measurements in the $B^0_s$ sector.

Determination of the CP-violating phase in $B^0_s \to J/\psi \phi$ decays at LHCb