ACR MDT ACFT FLC FAILED TO FOLLOW APCH CLRNC AND MAINTAINED THE WRONG HDG.

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FINAL LEG OF A 6 LEG 7 1/2 BLOCK HR DAY; ON DUTY FOR 10 HRS. FATIGUE WAS A FACTOR. ACR FLT NUMBER FROM ERIE; PA; TO DETROIT METRO. STARTED DSCNT CHKLIST INBOUND FROM SPICA. ONCE ON RADAR VECTOR HDG OF 270 DEGS I LEFT ATC FREQ TO CONTACT COMPANY. WHILE I WAS OFF FREQ; ATC ISSUED A CLRNC TO FLY HDG 240 DEGS (AS TOLD TO ME BY MY FO; WHICH I LATER FOUND OUT WAS A HDG TO INTERCEPT THE 21L LOC CLRNC; BUT MY FO ONLY UNDERSTOOD IT TO BE A HDG TO FLY WITH NO OTHER INSTRUCTIONS). WHEN I DIALED UP THE LOC FREQ UPON RETURNING FROM COMPANY I WAS FURTHER DISTRACTED FROM QUESTIONS FROM MY FO; WHO WAS NEW TO AIRLINE FLYING AND OUR COMPANY; 2 MONTHS SENIORITY. WHEN I FINALLY BEGAN TO EVALUATE OUR STATUS I NOTICED OUR POS WAS WELL TO THE W OF THE 21L LOC! I HAD A FULL SCALE DEFLECTION ON MY CDI. I THEN QUESTIONED MY FO AGAIN TO OUR CLRNC. AT THAT POINT; ATC ISSUED US A HDG OF 180 DEGS TO 'RE-INTERCEPT' THE LOC! THE FREQ WAS VERY BUSY AS THIS WAS A MAJOR RUSH TIME INTO DTW. WE TURNED TO 180 DEGS; BUT BEGAN TO TURN TO 210 DEGS QUICKLY BECAUSE THE FO THOUGHT HE WAS INTERCEPTING BECAUSE HIS CDI BEGAN TO CTR. (LATER TO FIND OUT HE HAD THE VOR FREQ IN; WHICH WOULD HAVE ALIGNED HIM WITH 21R). ATC; UPON NOTICING OUR ALIGNMENT WITH 21R; IMMEDIATELY ISSUED A HDG AND NOTIFIED US THEY WERE PULLING US OFF THE APCH. AT THAT POINT; I TOOK THE CTLS AND WE WERE VECTORED AROUND FOR THE APCH. CONTRIBUTING FACTORS: 1) FATIGUE. 2) POOR CREW COM. 3) POOR ATC/CREW COM. 4) MY ENTRUSTING A NEW FO WITH DUTIES THAT BECAME OVERWHELMING IN A TERMINAL AREA. 5) CHKLIST DESIGN AND COMPANY POLICY.