reserve th, th1, th2, th3 for Real;

theorem
  sin(th1)<>0 & sin(th2)<>0 implies cot(th1)+cot(th2) = sin(th1+th2)/(
  sin(th1)*sin(th2))
proof
  assume sin(th1)<>0 & sin(th2)<>0;
  then
  cot(th1)+cot(th2)= (cos(th1)*sin(th2)+cos(th2)*sin(th1))/(sin(th1)*sin (
  th2)) by XCMPLX_1:116
    .= sin(th1+th2)/(sin(th1)*sin(th2)) by SIN_COS:75;
  hence thesis;
end;
