B757-200 Captain reported an uncommanded steep turn of 45 degrees during departure climb. The Captain took control of the jet and returned to normal flight and followed by a crew debriefing the incident.

Narrative

Departing [Runway] XXR in ZZZ-ZZZ1. Tail Aircraft X. FO (First Officer) is Pilot Flying. I am Pilot (Captain) Monitoring. FMC programmed correctly. Cleared TO; ZZZZZ XX; cleared to 5000 ft. ZZZZ XX (alternate noise) climb out. LNAV armed. TO (takeoff); Center command at 200 ft. At 700 ft. AP commanded a turn to the right; more than a scheduled 90 degree turn; which is correct. At 1500 ft. AGL FO selected VNAV; on profile. Everything looks normal. As per SOP in ZZZ; it's an auto switch to Departure frequency. Approaching 2000 ft.; I look down at audio select panel to switch to Departure. Flick the switch; raise my left hand to the yoke to key mic. I started to talk and simultaneously looked back to FD. We were in a right hand approximately 40 degree bank. In a second we were at 45; and going further. The EGPWS warning came on. 'Bank Angle.' I clicked off AP; I said I have the jet. I recovered the aircraft. Returned it to normal flight and track. In a discussion with FO; I asked her if she saw that happening whilst I was heads down changing frequencies? Her statement was that she saw the bank angle going from 25 to 30 to 35 to 40 and beyond. She also states that she was curious to see if it would return to normal. She didn't intervene at all as she stated. I asked her at what point she would have intervened. Didn't really have an any. She did admit she should have intervened; or at least perhaps said something out loud whilst I was changing the radio. That she shouldn't have just sat there and done nothing.