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Strain plays an important role in Nb3Sn multifilamentary wires because critical current depends on it and strain sensitivity of Ic increases at higher magnetic fields. In this paper, a three-dimensional strain data set becomes available by further analysis of an earlier study of the Nb3Sn lattice parameter as a function of uniaxial applied strain at 4.2 K obtained by high-energy x-ray diffraction at the European Synchrotron Radiation Facility at Grenoble. Modeling of the angle dependence of the lattice strain with respect to the wire axis revealed that, under a specific angle, the cubic (undistorted) Nb3Sn unit cell is independent of the applied uniaxial strain. Knowing that the critical current has its maximum for an undistorted unit cell, it is suggested to put superconducting filaments close to this specific angle with the possibility to suppress, or at least reduce, the strain sensitivity of the critical current. For this purpose, a bronze route Nb3Sn wire was manufactured with various twist pitch lengths and with a maximum filament angle up to 38°. For the wire with the shortest twist pitch length (highest filament angle), the critical current at 19 T and 4.2 K is almost independent of the applied strain between 0.1% and 0.5%. This result confirms the theoretical/experimental considerations and opens a new way for the design and manufacture of Nb3Sn wires and magnets. [ABSTRACT FROM AUTHOR]