Let $(\tan \theta-1)(\sin \theta-\sqrt{3} \cos \theta)(\sin \theta+\sqrt{3} \cos \theta)=0$ i. State all possible values of $\tan \theta$. (1 mark) ii. Hence, find all possible solutions for $(\tan \theta-1)\left(\sin ^{2} \theta-3 \cos ^{2} \theta\right)=0$, where $0 \leq \theta \leq \pi$. (2 marks)

Step 1 ：\(\tan \theta = 1\)

Step 2 ：\(\sin \theta = \sqrt{3} \cos \theta\)

Step 3 ：\(\sin \theta = -\sqrt{3} \cos \theta\)

Step 4 ：\(\theta = \frac{\pi}{4}\)

Step 5 ：\(\cos \theta = \frac{1}{2}\)

Step 6 ：\(\theta = \frac{\pi}{3}\)

Step 7 ：\(\cos \theta = -\frac{1}{2}\)

Step 8 ：\(\theta = \frac{2\pi}{3}\)

Step 9 ：\(\boxed{\theta = \frac{\pi}{4}, \frac{\pi}{3}, \frac{2\pi}{3}}\)