Find the general values of `theta` from the following equations:
i) `sin3theta=sqrt(3)/2`, ii) `cos4theta=1/sqrt(2)`
iii) `tan2theta=sqrt(3)`
iv) `"cosec"3theta=2`

Explanation

To find the general values of \( \theta \) from the given equations, we will solve each equation step by step.

### i) Solve \( \sin(3\theta) = \frac{\sqrt{3}}{2} \)

1. **Identify the angle**: We know that \( \sin(\frac{\pi}{3}) = \frac{\sqrt{3}}{2} \).
2. **Set up the equation**: Since \( \sin(3\theta) = \sin(\frac{\pi}{3}) \), we can write:
\[
3\theta = n\pi + (-1)^n \cdot \frac{\pi}{3} \quad \text{for } n \in \mathbb{Z}
...