Rewrite "csc(theta)+sq rt2=0" as
1 1
-------------- = - ---------- = sin(theta). Because of the - sign we know that
csc(theta) sqrt(2) is in either Quadrant III or Quadrant IV.
If in Quadrant IV, the length of the hypotenuse is sqrt(2) and the opp. side is -1. This angle is -45 degrees, or +315 degrees. You could also find the negative angle that would give you this 45 45 90 triangle in Quadrant III.