If (A,B,C,theta) is a solution, then so is (tA,tB,tC,theta). This means that it won't be possible to find A, B and C (unless A=B=C=0), but finding theta might be possible.
If C<>0 then you can set C=1 because it won't make a difference to theta, and then try to find A, B and theta because you...