Prove that (1+ theta)/(1- theta) / (1- theta)/(1+ theta)=(4)/( theta theta). (ii) Hence solve for 0º < theta < 360º, the equation theta ((1+ theta)/(1- theta)-(1- theta)/(1+ theta))=3.

From part (i), we know that $\frac{1+\cos\theta}{1-\cos\theta} - \frac{1-\cos\theta}{1+\cos\theta} \equiv \frac{4}{\sin\theta \tan\theta}$.
Substitute this into the equation from part (ii):

$$\sin\theta \left(\frac{4}{\sin\theta \tan\theta}\right) = 3$$

$$\frac{4}{\tan\theta} = 3$$ $$\tan\theta = \frac{4}{3}$$

$$\theta = \arctan\left(\frac{4}{3}\right)$$ $$\theta \approx 53.1301^{\circ}$$

Since $\tan\theta$ is positive, $\theta$ lies in the first and third quadrants.
The first quadrant solution is:

$$\theta_1 \approx 53.13^{\circ}$$

The third quadrant solution is:

$$\theta_2 = 180^{\circ} + \theta_1$$ $$\theta_2 = 180^{\circ} + 53.13^{\circ}$$ $$\theta_2 = 233.13^{\circ}$$

The solutions are $\theta \approx 53.13^{\circ}$ and $\theta \approx 233.13^{\circ}$.

The final answer is $\theta \approx 53.13^{\circ}, 233.13^{\circ}$.