Timepix3 devices are hybrid pixel detectors developed within the Medipix3 collaboration at CERN providing a simultaneous measurement of energy (ToT) and time of arrival (ToA) in each of its 256$\times$256 pixels (pixel pitch: 55 µm). The timestamp resolution below 2 ns allows a measurement of charge carrier drift times, so that particle trajectories can be reconstructed in 3D on a microscopic level ($z$-resolution: 30-60 µm). The 3D trajectory reconstruction methodology developed elsewhere is validated against simulated data providing ground truth information of the incident angles. The detector response functions and the achievable track angular resolutions are determined. For the first time, data taken with Timepix3 in the MoEDAL experiment are presented. After extracting singly charged minimum ionizing particle (MIP) tracks from the mixed radiation field using characteristic track features, their impact angles are evaluated. The directionality of the MIP radiation field is shown in elevation angle ($\theta$) versus azimuthal angle ($\phi$) maps, "unfolded" using the simulated detector responses to an omnidirectional radiation field.