We report results of a systematic study of the anomalous low temperature state (LTS) angular magnetoresistance (MR) in the quasi-two dimensional organic conductor α-(BEDT-TTF) 2TlHg(SCN) 4 in fields up to 30 tesla. The high field suppression of the LTS is found to be independent of angle, while the MR maximum, H max increases with angle in conjuction with the well studied angular dependent magnetoresistance oscillations (ADMRO). The different magnetic breakdown probabilities above and below H max are found to be the source of a novel high field change in the ADMRO shape.