
theorem
  for A,B,C be Point of TOP-REAL 2 st angle(A,B,C) is non zero holds
  sin (angle(C,B,A)/3) =(sqrt 3 /2) * cos (angle(A,B,C)/3) + 1/2 *
  sin (angle(A,B,C)/3)
  proof
    let A,B,C be Point of TOP-REAL 2;
    assume angle(A,B,C) is non zero; then
    sin (1/3 * angle(C,B,A))
    = sin(2 * PI/3) * cos (1/3 * angle(A,B,C)) - cos ( 1/3 * 2 * PI) *
    sin (1/3 * angle(A,B,C)) by Thm26
    .=(sqrt 3 /2) * cos (angle(A,B,C)/3) + 1/2 * sin (angle(A,B,C)/3)
    by Thm14,Thm15;
    hence thesis;
  end;
