Question 215630
sin(theta)  =-1,,,,,taking  arc  sin
.
theta  = -90
.
from  base  of  360,  angle  = 360-90 = 270,,,,,check sin 270 = -1,,,ok
.
from  base  of  180 ,  angle  = 180-90=90,,,,,,checking  sin  90 = +1,,,,not  ok
.
Therefore  theta  is  270 degrees,  plus  all  rotations adding  360 degrees
.