B737 Captain reported encountering wake turbulence on arrival into DEN in trail of a B777 that resulted in an inflight upset.

Narrative

During flight there was forecasted and ATC advertised constant light turbulence in the descent as we crossed the Rocky Mountains. Because of this; I elected to have the passengers seated and the cabin crew prepare for arrival and take their seats prior to top of descent. Cleared to descend via FLATI3 Arrival and accomplished uneventfully with minimal turbulence. Subsequently cleared for the RNAV RNP Z 34R Approach while on the downwind; RF leg. While descending through approximately 7000 ft. with the autopilot engaged; we encountered a significant wake turbulence event. Abruptly; the airplane began to roll; we received both visual and aural 'roll authority' warnings and the autopilot disengaged. I immediately initiated upset recovery procedures. Was able to achieve a stable flight profile almost immediately. ATC notified us of a 777 eight miles ahead of us; which we had visual contact with. Upon notifying ATC of our event; they vectored the 777 off of the approach and cleared us in #1. Approach and landing was made without further event. Immediately following the event; FO made positive contact with cabin crew and confirmed the cabin was secure and there were no injuries. FO also stated that he felt that the aircraft rolled in excess of 60 degrees. I do not believe this was the case. Although this event was sudden and momentary; I did not observe any cockpit indications that would indicate a roll of that magnitude. Additionally; as a military instructor pilot who routinely flies in unusual attitudes; and increased bank angles; I perceived nothing to be abnormal or extravagant.Ultimately though; I am unsure if we exceeded an aircraft limitation. This event happened suddenly; unexpectedly; and was rectified almost immediately. In an attempt to execute the upset recovery procedure in the most expeditious manner; I did not visually take note of the max bank angle of the aircraft. My priority was simply to achieve a stable flight envelope.