Calculation trace with Mathematica
  
1 rotation qo

21.000000000000000000
19.000000000000000000

7 rotations q1

22.900000000000000000
16.900000000000000000

24.590000000000000000
14.610000000000000000

26.051000000000000000
12.151000000000000000

27.266100000000000000
9.5459000000000000000

28.220690000000000000
6.8192900000000000000

28.902619000000000000
3.9972210000000000000

29.302341100000000000
1.1069591000000000000

3 rotations q2

29.313410691000000000
0.81393568900000000000

29.321550047890000000
0.52080158209000000000

29.326758063710900000
0.22758608161110000000

7 rotations q3

29.326985649792511100
0.19825932354738910000

29.327183909116058489
0.16893233789759658890

29.327352841453956086
0.13960515398848053041

29.327492446607944566
0.11027780114702657433

29.327602724409091593
0.080950308700418629759

29.327683674717792011
0.051622705976009538166

29.327735297423768021
0.022295022301291746155


7 rotations q4

29.327737526925998150
0.019362248771549369353

29.327739463150875305
0.016429475018856769538

29.327741106098377191
0.013496701072541682007

29.327742455768484445
0.010563926961931844288

29.327743512161180638
0.0076311527163549958436

29.327744275276452274
0.0046983783651388777798

final 7th rotation

 X = 29.327744745114288787
 Y = 0.0017656039376112325524

rem Y/X = 0.000060202513113640101691

angle in radian = 1.5208379310730265893
angle in degre = 87.137594773892419676