B757 FLC ON VISUAL APCH SFO LOSES VISUAL CONTACT WITH SIDE-BY B777 AND INITIATES GAR.

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WE WERE ON A SCHEDULED FLT FROM IAD TO SFO. WE WERE RERTED BY ATC UP TO POINT REYES FOR 'SECTOR BALANCING' THEN VECTORED BY BAY APCH FOR AN UNCHARTED VISUAL APCH. CTLR POINTED OUT TFC; THEN TOLD US TO PROCEED DIRECT BRIJJ AND CLRED FOR VISUAL RWY 28R. NEAR BRIJJ; CTLR ASKED US TO LOOK FOR ADDITIONAL TFC; WHICH WE WERE UNABLE TO ACQUIRE BECAUSE OF HAZE. WE THEN REALIZED WE HAD LOST SIGHT OF PARALLEL TFC. WE LEVELED OFF AND TOLD THE CTLR WE WERE GOING AROUND. CTLR SAID THERE WAS NO NEED TO GO AROUND BECAUSE ADEQUATE SEPARATION EXISTS; BUT WE COULD GO AROUND IF WE WANTED TO; WHICH WE DID. THE CTLR GAVE US A HDG AND ALT AND THEN A FREQ CHANGE AND A SAFE GAR WAS ACCOMPLISHED. ADDING TO THE PROB WAS THE FACT THAT THE TFC IN CLOSE PROX TO US WAS TALKING TO A DIFFERENT CTLR ON A DIFFERENT FREQ. I THINK IT IS POSSIBLE TO MAINTAIN VISUAL SEPARATION FROM MORE THAN 1 ACFT. ALSO; A HIGH WORKLOAD SIT OF CONFIGURING THE AIRPLANE FOR LNDG AND MARGINAL VISUAL CONDITIONS ADD TO THE PROB. SUPPLEMENTAL INFO FROM ACN 476655: APCH POINTS OUT TFC (B777) ON EXTENDED FINAL FOR RWY 28L; 'PLAN TO FOLLOW TFC; CLRED VISUAL RWY 28R.' ADDITIONAL TFC FOR RWY 28R IS CALLED OUT BUT CANNOT BE SEEN DUE TO SUN IN OUR EYES. AS WE APCH BRIJJ; IT BECOMES OBVIOUS THAT OUR ASSIGNED SPD WAS NOT CAPABLE TO MAINTAIN A FOLLOWING POS WITH THE B777 WHICH HAD ALREADY SLOWED AND WAS TALKING TO SFO TWR. OUR FLT PATH RESULTED IN PASSING ABOVE AND IN FRONT OF THE B777.