  $\mu$TRISTAN is a realistic high energy lepton collider based on the existing
technology aiming at indirect and direct search for the physics beyond the
standard model (SM). We propose a measurement to determine one of the most
prominent parameters of the SM, weak mixing angle to test the SM and probe the
new physics effect in M\o ller-like scattering with a wide range of interaction
scales. We show that this experiment not only can determine the weak mixing
angle with percent to milli-level accuracy but also scan over a wide range of
interaction scales that have never been archived in a single experiment
elsewhere.
