B737-300 OVERSHOOTS FINAL GOING TO RWY 24R AT LAX. HAZY SKY CONDITIONS ADD TO FLC PROB OF SEE AND AVOID.

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WE WERE FLYING B737-300 ACFT ON VISUAL APCH TO RWY 24R AT LAX. FO WAS FLYING ACFT. WE WERE ASKED TO FOLLOW JETSTREAM ACFT THAT WAS ON BASE LEG; WE WERE ON DOWNWIND. TURNING TO FINAL OUR ACFT FLEW THROUGH CTRLINE TO RWY 24R. ANOTHER ACFT WAS ON BASE TO RWY 25L AND CAPT HAD THIS ACFT IN SIGHT AT ALL TIMES AND INSTRUCTED FO TO 'TIGHTEN UP BANK' WHICH HE DID AND RE-INTERCEPTED FINAL TO RWY 24R. DURING TURN TO FINAL WE HAD SINGLE RA 'MONITOR VERT SPD.' FO TRACKED CTRLINE AND COMPLETED STABLE APCH TO LNDG ON RWY 24R. WE RECEIVED NO ADVISORIES OR TFC INFO FROM ATC. CONTRIBUTING FACTORS INCLUDE HAZY CONDITIONS IN SMOG WITH SUN LOW IN SKY MAKING IT DIFFICULT TO MAINTAIN VISUAL WITH JETSTREAM WHILE LOOKING INTO SUN. I WOULD SUGGEST THAT DURING LATE AFTERNOON AND EARLY EVENING APCH CTL SHOULD VECTOR ACFT FOR ILS APCHS. ALSO THIS WAS LAST LEG OF 6 SEGMENTS THAT INCLUDED 2 SCHEDULED ACFT CHANGES WHILE TRYING TO MAINTAIN SHUTTLE TYPE TURN TIMES. THIS COULD HAVE CONTRIBUTED TO INCREASED CREW FATIGUE. FO HAD 150 HRS IN TYPE AND IN AIRLINE OPS IN GENERAL. DUTY DAY WAS 12 HRS 8 MINS.