Date: 201510
Local time of day: 0601-1200
Location: MGGT.Airport, FO
Flight conditions: VMC
Light: Daylight
Aircraft: B767-300 and 300 ER
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Flight phase: Initial Approach
ATC / advisory: TRACON MGGT
Second aircraft: B737 Undifferentiated or Other Model
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Second reporter function: First Officer; Pilot Flying
Anomaly: ATC Issue All Types; Aircraft Equipment Problem Less Severe; Conflict Airborne Conflict; Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Clearance
Detector: Automation Aircraft RA; Person Flight Crew
When detected: In-flight
Result: Air Traffic Control Issued New Clearance; Flight Crew FLC complied w / Automation / Advisory; Flight Crew Executed Go Around / Missed Approach
Contributing factors: Aircraft; Airport; Procedure
Primary problem: Ambiguous

Narrative: Prior to initial descent we had planned on an ILS Z approach to runway 02; MGGT.  After reviewing the arrival angles; (we were arriving from the SW; and the course reversal turn would be greater than 170 degrees) I; Pilot Not Flying (PNF) advised that it would be easier to fly the ILS Y.  The Pilot flying (PF) agreed and we reprogrammed and reviewed the differences for this approach.  When we were turned over to the local controller we requested the ILS Y. ATC advised that it was not available due to local VFR traffic and we were then assigned a delaying vector downwind; slowed to 210 kts; and advised us of traffic at 10 o'clock and X miles.  During this vector we rebuilt for the ILS Z approach and visibly acquired the traffic passing to [our] left.  A few moments later we were cleared direct the AUR VOR and the ILS Z approach. We crossed the AUR VOR (initial approach fix) at 9;000 feet autopilot on; LNAV; VNAV engaged; and selected 6;300 feet in the MCP.  The approach was monitored using the automation and raw data; with no anomalies noted.  The aircraft was set to join the LOC just outside the FAF at an altitude of 6;300 feet.  The autopilot started the turn just prior to the 5 DME fix listed on the approach; observed at about 4.9 miles from the AUR VOR via raw data.  As we rolled through about 90 degrees to the final we; both PF and PNF; observed a B737 on final in front and below us.  We advised ATC that we were going missed approach and initiated the procedure. During the missed approach procedure we received a climb TCAS RA.  We advised ATC and the B737 that we had them in sight and were climbing to 9;000 feet; the MAP altitude; and rolled wings level.After the TCAS RA was resolved we began a right turn direct to the AUR VOR; away from the high terrain we had briefed; and along the missed approach path. While in the turn the bank angle increased beyond 30 degrees and we received an aural 'Bank Angle' warning.  The bank angle was never observed over 40 degrees and was corrected immediately to below 30 degrees. After passing the AUR VOR; ATC then cleared us back for another uneventful approach and landing.At no time were we instructed to follow the B737; advised of spacing; or given a speed to maintain during the approach. We were under the impression that the B737 was not a factor and that aircraft was already on the ground.  The only time we were contacted by ATC; after being cleared for the approach; was after we advised them that we were going missed approach. After we were in the gate we contacted the B737 crew and informed them that we had received a TCAS RA; but that we had a visual on them just prior to the warning.  They said they had also had received a TCAS descending RA and had descended only a few hundred feet.  ATC did not comment on the event.Upon block in we did notice a map shift [between the FMC position and Gate position].


Second narrative: [Report narrative contained no additional information.]


Synopsis: A B767 flight crew; flying the ILS Z RWY 2 at MGGT; experiences a TCAS RA with a B737 flying the ILS Y. The B767 crew may have performed the course reversal early due to a small IRS error; but ATC never advised the crew of the B737 traffic. A go-around is initiated by the B767 crew. During the go-around; a 30 degrees bank angle is exceeded momentarily triggering a bank angle warning.