sin(pi/6-a)=1/3,则cos(2pi/3+2a)的值为

∵sin(π/6-α)=1/3
∴cos[2(π/6-α)]=1-sin²(π/6-α)=7/9
即cos(π/3-2α)=7/9
cos(2π/3+2α)=cos[2(π/3+α)]
=cos[2(π/2-π/6+α)]
=cos[π-(π/3-2α)]
= -cos(π/3-2α)
=-7/9