∵2sin(α/2+π/6）=1/2
∴sin(α/2+π/6）=1/4

∴cos(π/3+α)
=cos[2(α/2+π/6)]
=1-sin²(α/2+π/6）
=1-2*1/16=7/8

∴sin(6/π-α)
=sin[π/2-(π/3+α)]
=cos(π/3+α)
=7/8