PLT FLYING A MISSED APCH HAD A NEAR MISS IN VFR CONDITIONS. THE RPTR FELT THE TWR SHOULD HAVE PROVIDED A TA.

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MY MISSED APCH INSTRUCTIONS WERE TO FLY A HDG OF 180 DEGS AT 2500 FT. AS I FLEW THROUGH THE DECISION HT OF 662 FT AND HAD BEEN CLRED FOR THE OPTION; I CLBED TO 1500 FT MSL ON THE RWY HDG; TURNED TO A HDG OF 180 DEGS AND CONTINUED TO CLB. AS I APCHED 1700 FT MSL; A TWIN ENG PLANE IN THE LNDG PATTERN (WITH WINGLETS ON ITS WINGTIPS) WAS IN MY CLB PATH. MY SAFETY PLT SAID 'TURN R; THERE'S A PLANE.' I FLIPPED UP MY VIEW RESTRICTING DEVICE; SAW THE PLANE; DIVED AND TURNED R JUST AS THE TWIN IN THE PATTERN ALSO ROLLED R; AS IT PASSED FROM R TO L IN FRONT OF US. CONTRIBUTING FACTORS: 2 OTHER PLANES WELL AHEAD OF THE TWIN APPEARED TO HAVE SOMEHOW GOTTEN SO CLOSE THEY APPEARED TO BE FLYING FORMATION FOR A LNDG. THE SAFETY PLT WAS DISTR BY THE PLANES AND THE CHATTER WITH THE TWR CTLR TRYING TO SEPARATE THEM. SHE WAS UNABLE TO ADVISE THE TWR OF OUR MISSED APCH. THE TWIN WAS GIVEN INSTRUCTIONS FOR PATTERN ENTRY AND WAS NOT VISIBLE AT THAT TIME. OUR COCKPIT RESOURCE MGMNT COULD HAVE BEEN BETTER IF SHE TOOK CTL; BUT SHE WAS SURPRISED BY THE TWIN'S FAST PATTERN SPD; AND NOT ACCUSTOMED TO TAKING CTL OF THE PLANE. WE PLAN TO TRY PRACTICING THIS; WITH MORE DISTANCE PLANES. I WONDERED WHETHER THE TWR CTLR LOST SIGHT OF OUR PLANES; WHILE TRYING TO SEPARATE THE OTHER TWO. I DON'T KNOW IF HIS BRITE RADAR WAS OPERATING OR NOT. IF IT WAS; HE MIGHT NOT HAVE GLANCED AT IT; OR NOT SEEN THE CONFLICT.