We report results of a systematic study of the anomalous low temperature state (LTS) angular magnetoresistance (MR) in the quasi-two dimensional organic conductor alpha-(BEDT-TTF)(2)TlHg(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 conjunction 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.