C650 CREW AND A C310 HAD LESS THAN LEGAL SEPARATION IN PVD CLASS C.

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APCH INITIAL ADVISED US TO PLAN ON THE VOR 23 APCH. WE WERE BEING VECTORED FOR DOWNWIND WHEN ALL OF A SUDDEN APCH GAVE US A TURN TOWARDS THE ARPT AND ASKED US TO RPT IT IN SITE (IT WAS CURRENTLY 3 MI IN HVY HAZY). AFTER ABOUT ONE MIN HE GAVE US ANOTHER VECTOR AWAY FROM THE ARPT AT WHICH TIME I ADVISED I HAD THE RWY IN SIGHT. HE SAID WAIT A MIN I HAVE TO CALL GROTON TWR. SO I CONTINUED TOWARD THE RWY. WE WERE HIGH SO I HAD TO SLOW DOWN GET DIRTY AND GET A GOOD DSCNT RATE GOING. WE WERE ON A 2.0 MI FINAL WHEN WE FINALLY CHKED IN AT ABOUT THAT TIME THE TCASII SAID 'TFC TFC.' AT WHICH TIME I LOOKED DOWN AND TO MY L; THERE WAS A CESSNA 310 TURNING A CLOSE IN BASE TO FINAL. TWR THEN ADVISED HE HAD BOTH OF US IN SITE; SO I IMMEDIATELY PULLED UP AND CIRCLED TO THE R. TWR FIGURED OUT THE OTHER ACFT WAS VFR AND DUE TO RADAR COVERAGE; PVD APCH HAD NO IDEA HE WAS THERE. I WAS VERY UPSET WITH MYSELF ON THIS. I FELT ONE; APCH CTLR LEAD ME INTO THIS AND I BITE HOOK LINE AND SINKER. I HAD JUST FINISHED READING YOUR MAY ISSUE ABOUT UNSTABILIZED APCHS. I SHOULD OF KNOWN BETTER. NEXT TIME AROUND I WILL BE STICKING WITH THE VOR 23 APCH AND WON'T LET SOMEONE ELSE TALK ME INTO SOMETHING.