A FATIGUED FLC CONFUSES THEIR DSCNT CLRNC INTO LAS CAUSING A NAV DEV.

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NEAR 'LIDAT' INTXN (BTY 310 DEGS AT 45 DME) SEBOUND; CURRENT CLRNC WAS DIRECT BTY BTY.FUZZY3 LAS. CTLR CLRED US TO CROSS 'FUZZY' AT FL180; DISCRETION; AT 'FUZZY' FLY HDG 120 DEG VECTORS FOR THE VISUAL. WE WERE IN OUR 13TH HR OF DUTY -- FATIGUED -- LAST LEG. DUE TO THE DISTANCE WE WERE FROM BTY WHEN ISSUED THE CLRNC -- SOMEWHERE BEFORE REACHING BTY VOR I THOUGHT THE VECTOR HDG WAS AT THE NEXT FIX; BTY VICE FUZZY. SO; REACHING BTY VOR I STARTED FLYING HDG 120 DEGS (NOT FOLLOWING THE 115 DEG RADIAL ON THE STAR). A FEW MINS LATER ZLA ASKED; 'DO YOU SHOW YOURSELF ON COURSE?' THE CAPT DURING THIS WHOLE TRANSITION WAS GETTING ATIS AND TALKING TO COMPANY. HE JUST TOLD ME HE WAS BACK ON ATC FREQ; WHEN HE HEARD THIS QUESTION. HE DID NOT IMMEDIATELY ANSWER ATC AND I TOLD HIM; VERY CONFIDENTLY; THAT WE WERE FLYING HDG 120 DEGS (I STILL THOUGHT WE WERE FOLLOWING THE CLRNC). CTR THEN SAID 'YOU'RE ABOUT TO ENTER RESTR AIRSPACE; TURN R 10 DEGS TO JOIN THE ARR.' I THEN TURNED TO HDG 140 DEGS TO JOIN; REALIZING 10 DEGS WOULD NOT WORK AT ALL. THEN CTR SAID; 'FLY HDG 150 DEGS TO REJOIN.' CTR THEN ASKED IF WE WERE FLYING 120 DEGS PREVIOUSLY AND THE CAPT RESPONDED; 'SORRY FOR THE CONFUSION.' FACTORS -- PURE FATIGUE. I KNOW CTR SAID FUZZY; BUT THAT FUZZY WAS A DIFFERENT FUZZY IN MY HEAD -- BTY. ALSO CAPT WAS OFF GETTING ATIS AND THE COMPANY CALL.