I'm making a few assumptions in asking my question. If they're incorrect, please comment.
Tefillat Shacharit is a substitute for the Shacharit sacrifice that was brought in the Temple. I have also heard that there was a time when people wore Tefillin the entire day, and at some point, this was scaled back to wearing it during the Shacharit prayers.
During the time of the Temple services, when did people wear tefillin? Was it the entire day, then? Does this mean that Cohanim wore tefillin while they were offering the sacrifices?
Between the time of the Temple destruction and the standardization of a Shacharit service as we have it, today (i.e. a specific order of prayers that we are currently saying), (by "destruction, I include the period between end of 1st and completion of the 2nd as well as after destruction of the 2nd.) when did people wear tefillin?