Determining Weak-Mixing Angle at $\mu$TRISTAN

$\mu$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mixing angle with percent to milli-level accuracy but also scan over a wide range of interaction scales that have never been archived in a single experiment elsewhere.