设u=a+π/6,2a+π/12=2u-π/4,cosu=-1/3,sinu=土2√2/3,sin2u=2sinucosu=干4√2/9,cos2u=2(cosu)^2-1=-7/9,sin(2a+π/12)=sin(2u-π/4)=(sin2u-cos2u)/√2=(7√2干8)/18.