sinα+cosα=√2/3
(sinα+cosα)^2=2/9
sin^2α+cos^2α+2sinαcosα=2/9
2sinαcosα=-7/9
sin2α=-7/9
由万能公式可得
sin2α=2tanα/(1+tan^2α)=-7/9
18tanα=-7(1+tan^2α)
7tan^2α+18tanα+7=0
tanα=(-18±8√2)/14==(-9±4√2)/7