Falcon 900 Captain reported temporary loss of aircraft control while level in cruise and both pilots heads down doing the approach briefing.

Narrative

I got up for work at XA:00 A.M. We would have four legs that day from our home airport; ZZZ; to ZZZ1; to ZZZ2; back to ZZZ1; then return home to ZZZ. Put the airplane to bed; drive home and back in the bed at XB:00 PM. Toward the end of a nineteen hour day on the last leg from ZZZ1 to ZZZ we were cruising at 40;000 feet at night with no weather and smooth air. With 30 minutes to go; I decided to brief the approach into ZZZ; with the other pilot. With our heads down looking at the iPad in my lap we began the approach briefing. The next thing I hear is the over-speed warning going off. I look up and we are in a nose low; 30-degree bank to the right. I've got a real life unusual attitude at 40;000 feet at night! It was reflex to come back on the throttles; level the wings; pitch the nose up and climb back to 40;000 feet and get back on course. I was hoping that ATC didn't notice; but how could they not notice? By the time the over-speed warning went off; I lost 1200 feet of altitude and turned about 30-degrees off course. They said nothing. I said nothing. The adrenaline rush kept me alert for the rest of the flight. I am confident that fatigue was the main contributing factor. We need to impose a shorter work day on ourselves. Plus; at the end of a long day at altitude; breath some Oxygen to refresh ourselves. The rest of the flight was uneventful.