TRISLANDER CREW HAD AN NMAC IN S46 CLASS E AIRSPACE IN IMC WITH AN ACFT NOT ON AN IFR FLT PLAN.

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DEPARTING BREMERTON XA20 LNDG RWY 19 ON AN IFR CLRNC. ON THE GND AT PWT; I LISTENED TO THE BFI ATIS THEN THE LCL AWOS AND CALLED SEATTLE FOR AN IFR CLRNC. I WAS INSTRUCTED TO CONTACT DEP 120.1 IN THE AIR; L TURN TO 100 DEGS; MAINTAIN 2000 FT. I KEPT COM #2 ON 120.1 AND SWITCHED TO COM #1 123.05 (LCL). I ANNOUNCED MY INTENTIONS. I MONITORED THE 123.05; NEVER HEARD ANY REPLY. I SCANNED THE AREA AND TAXIED ONTO RWY 19.; ANNOUNCED MY TKOF WITH A L TURNOUT. AS I WAS CLBING THROUGH 1000 FT; I BEGAN THE L TURN AND SWITCHED TO COM #2 (WHILE CONTINUOUSLY MONITORING COM #1). ATC SAID 'RADAR CONTACT; MAINTAIN 3000 FT.' AS I WAS CLBING THROUGH 1500 FT HDG 100 DEGS; ATC CALLED TFC 1 MI; 2 O'CLOCK POS; 1700 FT. I WAS ABOUT 200 FT FROM ENTERING CLOUDS; BUT I TOLD THEM I SAW THE TFC. THE ACFT APPEARED TO BE AT MY ALT AND DSNDING. ATC TOLD ME TO MANEUVER AS REQUIRED. I DETERMINED THAT SINCE I WAS CLBING AT GREATER THAN 1000 FPM; AND THEY WERE DSNDING; IT WOULD BE BEST TO CONTINUE. AS I ENTERED THE CLOUDS APPROX 1700 FT MSL; I SAW THE OTHER ACFT GO JUST BEHIND AND WHAT APPEARED TO BE MORE THAN 500 FT BELOW ME. I WAS IMC ONLY A MOMENT LATER. I TOLD ATC THE TFC CLRED BELOW. A MOMENT LATER I HEARD THE ACFT CALL DOWNWIND; THEN BASE AND FINAL. FORTUNATELY; DUE TO THE CTLR'S VIGILANCE AND MY GOOD CLB RATE; WE WERE ABLE TO AVOID A CONFLICT. HOWEVER; I THINK IT MUST BE STRESSED THAT THOUGH AN ARPT IS UNCTLED; THERE CAN STILL BE A MIX OF IFR AND VFR BUSY TFC. VFR TFC MUST UNDERSTAND THAT TALKING ON THE RADIO CAN SAVE LIVES. PLEASE CALL 10 MI OUT; THEN 5 MI WITH INTENTIONS. AND COMPLY WITH CLOUD CLRNC REQUIREMENTS. IFR TFC MUST ASSUME THAT OTHER ACFT ARE OPERATING WITH NO RADIO; AND BE EXTREMELY VIGILANCE.