Or my way:-
Assume nil wind
TAS=G/S=230kt
1%=2.3nm
Now, if you wait till 2.3nm prior to start your turn onto the DME arc, you'll be as near as damn it due to inertia of the a/c.
In any event you'll be within the tracking tolerances (2nm) by a good margin.
K.I.S.S.
