This thesis project concerns the precise measurement of the electroweak mixing angle with the ATLAS experiment, at the LHC. The evolution with energy of this fundamental parameter will also be tested. The measurement will be based on the di-muon data set from runs 2 and 3 of the LHC, and will use the muon spectrometer as the main instrument.

The determination of the mixing angle is based on the measurement of the forward-backward asymmetry of the Z boson decay muons. For precise control of systematic uncertainties, the internal alignment of the spectrometer must be optimized. This alignment constitutes an important part of the project. The performance of the New Small Wheel, the new muon detector installed for run 3, will also need to be understood in detail. The actual measurement will be carried out at the end of these preliminary studies, and an interpretation of the result will complete the thesis.