cos(2α+π/3)=cos[2(α+π/3)-π/3]=cos(2(α+π/3))*cos(π/3)+sin(2(α+π/3))*sin(π/3)
cos(2(α+π/3))=2cos^2(α+π/3)-1=2*1/16-1=-7/8
sin(α+π/3)=正负根号(1-1/16)=正负根号15/4
sin(2(α+π/3))=2cos(α+π/3)*sin(α+π/3)=正负根号15/8
所以答案是（-7+3*根号5）/16,或者 （-7-3*根号5）/16