
theorem Thm5:
  for a be Real holds sin (2*PI/3 - a) = sin (PI/3 +a)
  proof
    let a be Real;
    sin (2*PI/3 - a) = sin (PI - (PI/3+a))
    .= sin PI * cos (PI/3 + a) - cos PI * sin (PI/3+a) by SIN_COS:82
    .= sin (PI/3 + a) by SIN_COS:77;
    hence thesis;
  end;
