  Flavour-tagged, time-dependent, angular analysis of the decay $B^0_s \to
J/\psi \phi$ allows the determination of a CP-violating phase which in the
Standard Model is denoted $-2\beta_s$, and is predicted to be very small. Many
models of new physics lead to significant enhancements in the value of this
observable. LHCb has the capability to improve significantly the existing
experimental 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 of
operation. The steps in this measurement programme will be presented.
Discussion will also be given to other methods to determine this phase, and
related measurements in the $B^0_s$ sector.
