由上式变形可得：cos^4 a+cos^2 a-4/9=0.
解之得：cos^2 a=1/3或-4/3（舍）.则有sin^2 a=1-cos^2 a=2/3.
又由a是第3象限角,故cosa=-√3/3,sina=√6/3,
sin2a=2sinacosa=2√2/3.