- (a) Prove that
$$\tan \theta + \cot \theta \equiv 2 \operatorname { cosec } 2 \theta , \quad \theta \neq \frac { n \pi } { 2 } , n \in \mathbb { Z }$$
(b) Hence explain why the equation
$$\tan \theta + \cot \theta = 1$$
does not have any real solutions.