reserve th, th1, th2, th3 for Real;

theorem
  tan(-th) = -tan(th)
proof
  tan(-th) = sin(-th)/cos(th) by SIN_COS:31
    .= (-sin(th))/cos(th) by SIN_COS:31
    .= -tan(th) by XCMPLX_1:187;
  hence thesis;
end;
