I noted that the sequence
89
89.9
89.99
89.999
is 90 minus
1
0.1
0.01
0.001
or, in other words:
90 − 100
90 − 10−1
90 − 10−2
90 − 10−3
and that, furthermore, that negative power was the same as the positive power you had to divide tan by to get 180 / π.