Prove trigonometric identity

1. (i) Showing each step in your reasoning, prove that

$$( \sin x + \cos x ) ( 1 - \sin x \cos x ) \equiv \sin ^ { 3 } x + \cos ^ { 3 } x$$ (ii) Solve, for \(0 \leqslant \theta < 360 ^ { \circ }\), $$3 \sin \theta = \tan \theta$$ giving your answers in degrees to 1 decimal place, as appropriate.
(Solutions based entirely on graphical or numerical methods are not acceptable.)

4. (i) Prove, by counter-example, that the statement $$\text { " } \sec ( A + B ) \equiv \sec A + \sec B , \text { for all } A \text { and } B \text { " }$$ is false.
(ii) Prove that $$\tan \theta + \cot \theta \equiv 2 \operatorname { cosec } 2 \theta , \quad \theta \neq \frac { n \pi } { 2 } , n \in \mathbb { Z }$$