theorem
  sin(th+2 * PI) = sin(th) & cos(th+2 * PI) = cos(th) &
  sin(PI/2-th) = cos(th) & cos(PI/2-th) = sin(th) & sin(PI/2+th) = cos(th) &
  cos(PI/2+th) = -sin(th) & sin(PI+th) = -sin(th) &
  cos(PI+th) = -cos(th) by Th77;
