答：sin(π/6-a)=1/3sin(a-π/6)=-1/3cos(2π/3+2a)=cos(π-π/3+2a)=-cos(π/3-2a)=-cos[2(a-π/6)]=-1+2*{sin(a-π/6) ]^2=-1+2*(-1/3)^2=-1+2/9=-7/9
