reserve p1,p2,p3,p4,p5,p6,p,pc for Point of TOP-REAL 2;
reserve a,b,c,r,s for Real;

theorem Th1:
  sin angle(p1,p2,p3) = sin angle(p4,p5,p6) & cos angle(p1,p2,p3) =
  cos angle(p4,p5,p6) implies angle(p1,p2,p3) = angle(p4,p5,p6)
proof
A1: 2*PI*0<=angle(p1,p2,p3) & angle(p1,p2,p3)<2*PI+2*PI*0 by COMPLEX2:70;
A2: 2*PI*0<=angle(p4,p5,p6) & angle(p4,p5,p6)<2*PI+2*PI*0 by COMPLEX2:70;
  assume sin angle(p1,p2,p3) = sin angle(p4,p5,p6) & cos angle(p1,p2,p3) =
  cos angle( p4,p5,p6);
  hence thesis by A1,A2,SIN_COS6:61;
end;
