B737 FLT CREW EXPERIENCED TCAS RA AT APPROX FL360 WHEN ZDC CTLR ISSUED DSCNT CLRNC THROUGH OCCUPIED ALT; OPERROR RECORDED.

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WE WERE IN CRUISE AT FL370. JUST PRIOR TO ASBUR INTXN; WE WERE GIVEN A CLRNC TO DSND AND MAINTAIN FL350. THE FO PROGRAMMED THE AUTOPLT FOR THE DSCNT AND BOTH HE AND I CONFIRMED THE CLRNC VERBALLY WHILE POINTING AT THE SELECTED ALT. SHORTLY AFTER LEAVING FL370; WE RECEIVED A TCAS TA. THE FO LEVERED THE ACFT AS THE DSCNT STOPPED WE RECEIVED A TCAS RA. THE FO DISCONNECTED THE AUTOPLT AND STARTED FOLLOWING THE ADVISORY GUIDANCE IN A CLB. ZDC QUERIED OUR ALT; AND I RESPONDED FL365. IN FACT THE DSCNT BOTTOMED AT FL366! THERE WAS TFC INDICATED ON OUR NAV SCREEN 600 FT BELOW US AT APPROX OUR 4 O'CLOCK POS. WE RECEIVE INSTRUCTIONS FROM ATC TO CLB TO FL370. SHORTLY AFTER LEVELING AT FL370 WE WERE GIVEN INSTRUCTIONS TO MAINTAIN FL330. THE SUBSEQUENT DSCNT AND ARR AT OUR DEST WAS UNEVENTFUL. UPON ARR; I CONTACTED THE SUPVR AT ZDC. HE STATED THAT THE CTLR HAD DSNDED US INTO TFC AT FL360. HE WAS VERY HELPFUL AND EXPLAINED HOW THE SITUATION HAD OCCURRED. THE FLT ATTENDANTS AND THE PAX WERE UNAWARE OF THE INCIDENT. THE FO PERFORMED THE LEVELOFF AND CLB SMOOTHLY; FOLLOWING THE RA INSTRUCTIONS PRECISELY. IN RETROSPECT; I COULD HAVE SEEN THE TFC ON THE TCAS SCREEN. NEITHER THE FO NOR I WERE DISTR. BOTH OF US HAD OUR NAV DISPLAYS SET TO LONG RANGE WHICH MAY HAVE MADE IT MORE DIFFICULT TO IDENT THE TFC.