(a) Where \(\cos\theta\ne0\), \[\tan^4\theta-1=\frac{\sin^4\theta-\cos^4\theta}{\cos^4\theta}=\frac{(\sin^2\theta-\cos^2\theta)(\sin^2\theta+\cos^2\theta)}{\cos^4\theta}=\frac{1-2\cos^2\theta}{\cos^4\theta}.\]

(b) \[\frac{1-2\cos^2\theta}{\cos^2\theta}=7\Rightarrow\cos^2\theta=\frac19.\] Thus \(\theta=70.5^\circ,109.5^\circ\). The expression is undefined at \(90^\circ\).