we know that
sin theta = -0.8190
then
theta=arc sin (-0.8190)------> using a calculator-----> theta=-54.98
theta=-55 degree
the theta angle could belong to the third or fourth quadrant
case a) theta belong to the IV quadrant
so
theta=360-55-----> theta=305°
case b) theta belong to the III quadrant
so
theta=180+55-----> theta=235°