AN ACR WDB FLC TURNED TO THE WRONG HDG WHEN THE CAPT MISUNDERSTOOD THE CLRNC.

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WE DEPARTED SJC ON THE LOUPE 9 DEP AND HAD ESTABLISHED ON THE 339 DEG RADIAL FROM SJC. DEP CTL GAVE US A 010 DEG HDG FOR LINDEN. WE INDICATED THAT WE COULD PROCEED DIRECT LINDEN ON THE INS IF DESIRED. I THOUGHT HE CLRED US DIRECT TO LINDEN 20 DEGS TO OUR R. WE TURNED 20 DEGS TO THE R AND PROCEEDED INS DIRECT LINDEN. THE CTLR QUESTIONED OUR HDG AND WE CONFIRMED DIRECT TO LINDEN; HOWEVER; THE FO INFORMED ME WE WERE TO BE CLRED DIRECT LINDEN AFTER 20 MI (NOT DEGS AS I HAD THOUGHT). I SHOULD HAVE LISTENED CLOSER AND VERIFIED CLR DIRECT (ALTHOUGH I THOUGHT I HAD). CONTRIBUTING FACTOR WAS FATIGUE AND THE DISTR OF A SEAT THAT WOULD ONLY MOVE FURTHER FORWARD (ELECTRICALLY) AND NOT BACK. SUPPLEMENTAL INFO FROM ACN 380055: DEPARTING SJC (LOUPE 9 DEP) OUT OF APPROX 14000 FT; ZOA ADVISES TO FLY HDG 010 DEGS FOR LINDEN VOR. AFTER ABOUT 60 SECONDS; I NOTICED IT WOULD TAKE ABOUT 030 DEGS TO GO TO LINDEN VOR. CALLED ATC AND ADVISED THAT WE WERE RECEIVING LIN AND DID HE WANT US TO GO DIRECT TO LINDEN. HE SAID NO; NOT FOR ABOUT 20 MI. PF UNDERSTOOD THIS TO MEAN; YES GO DIRECT LINDEN. FO FAILED TO XCHK AND NOTICE THE SMALL HDG CHANGE OF 20 DEGS AS PF WENT DIRECT TO LIN VOR. ATC CALLED US BACK TO ASK IF WE WERE STILL FLYING 010 DEGS ASSIGNED HDG. WE SAID NO; GOING DIRECT LIN VOR. CTLR THEN GAVE US A FREQ CHANGE. UPON CALLING NEW FREQ WE WERE THEN CLRED DIRECT LIN. AFFECTING FACTORS: BUSY DEP AND NON STANDARD. SUN ANGLE VERY LOW; BOTHERSOME. CONFUSING ATC ROUTING 'FLY 010 DEGS FOR LINDEN.' BUSY ATC FREQ.