A B767 FLC WAS INCAPABLE OF FLYING THE ASSIGNED DEP FROM LAX.

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PREFLT; TAXI; AND TKOF WAS NORMAL OTHER THAN THE MIXED CREW. CAPT WAS FROM MIA; FO WAS FROM LAX; AND FLC WAS FROM ORD. GORMAN 2 DEP; WHICH HAD NEVER BEEN FLOWN BY ANY OF THE PLTS ON BOARD; WAS FLOWN. PF WENT RWY HDG UNTIL TOLD BY ZLA TO TURN R HDG 360 DEGS AND CLB TO 9000 FT. AFTER TURN WAS MADE; PF DIRECTED PNF TO ARM LNAV; WHICH PNF DID. ATC TOLD FLT TO INTERCEPT THE GORMAN 2 DEP. BOTH HSI'S WERE SET ON A VERY SMALL SCALE AND GORMAN WAS NOT VISIBLE ON EITHER SCREEN. A MAGENTA LINE APPEARED AND PF FOLLOWED IT TO A HDG OF 270 DEGS. AFTER APPROX 1-2 MINS; ATC ASKED FLT WHAT ITS HDG WAS AND THAT WE WERE SUPPOSED TO BE HDG 360 DEGS UNTIL INTERCEPTING THE DEP. PF ENGAGED HDG SELECT AGAIN AND TURNED TO 360 DEGS. ATC THEN TOLD FLT TO COME FURTHER R TO 060 DEGS; WHICH PF DID. FLT WAS CHASTISED BY ATC AND THEN GIVEN TA'S OF A DC10 AT 12 O'CLOCK AND 1 MI; 1000 FT ABOVE. TFC WAS IN SIGHT AND FLT GOT BACK ON THE DEP WITHOUT FURTHER PROBS. NONE OF THE FLC COULD FIGURE OUT WHERE THE EXTRANEOUS MAGENTA LINE EVER CAME FROM OR WAS GOING TO. THIS WAS AN ACFT WHICH HELPED TO CONFUSE ALL PLTS JUST ENOUGH SO THAT OUR SITUATIONAL AWARENESS WAS SLIGHTLY REDUCED. SUPPLEMENTAL INFO FROM ACN 457711: THE LNAV INTERCEPTED A STRAY PINK LINE (I HAVE NO IDEA WHERE IT CAME FROM) AND TURNED TO 270 DEG HDG AND FOLLOWED IT. QUERIED BY ATC ABOUT HDG AND CONFUSION ABOUT RTE; WE WENT 200 FT PAST 9000 FT (OUR LEVELOFF ALT). IN THE FUTURE; I WILL ALWAYS HAVE A RAW DATA BACKUP DISPLAYED; EVEN AT THE VERY FAMILIAR ARPTS.