Multiply by \(\tan^2\theta\ne0\): \[3\tan^4\theta+\tan^2\theta-2=0\quad\Longrightarrow\quad(3\tan^2\theta-2)(\tan^2\theta+1)=0.\] The second factor cannot vanish for real \(\theta\). Therefore \(\tan\theta=\pm\sqrt{2/3}\). The solutions in the interval are \(\boxed{39.2^\circ,140.8^\circ}\); \(90^\circ\) is excluded because tangent is undefined.