In self-induced-transparency (SIT) mode locking, 2πSIT solitons with a duration much smaller than the polarization relaxation time T2 in the gain and absorber are formed in a laser cavity. This is in contrast to standard passive mode-locking schemes based on gain and absorption saturation. Despite the great promise, up to now SIT mode locking with 2πpulses was mainly studied theoretically. In this paper, a stable self-starting passive mode locking is demonstrated experimentally in a Ti:sapphire laser with a Rb vapor cell. We show that the mode locking indeed appears to be due to SIT in the Rb cell; that is, the pulse in the Rb cell is a 2πSIT soliton. We also confirm self-starting of the SIT mode locking. Self-starting takes place via a set of intermediate regimes, including the one containing zero-area pulses.