reserve a, b, c, d, x, y, z for Complex;
reserve r for Real;

theorem Th78: :: COMPLEX2:47, 48
  angle(a,b,c) <> 0 iff angle(a,b,c)+angle(c,b,a) = 2*PI
proof
  hereby
    assume angle(a,b,c) <> 0;
    then angle(c,b,a) = 2*PI-angle(a,b,c) by Lm4;
    hence angle(a,b,c)+angle(c,b,a) = 2*PI;
  end;
  assume angle(a,b,c)+angle(c,b,a) = 2*PI & angle(a,b,c) = 0;
  hence contradiction by Th68;
end;
