Solve the following trigonometric equations: `s intheta/2=-1` (ii) `cos(3theta)/2=1/2` (iii) `t a n(2/3theta)=sqrt(3)`

Explanation

Let's solve the given trigonometric equations step by step.

### (i) Solve `sin(theta/2) = -1`

1. **Identify the angle where sine is -1**: The sine function equals -1 at specific angles. The primary angle where this occurs is:
\[ \frac{\theta}{2} = \frac{3\pi}{2} + 2k\pi \quad (k \in \mathbb{Z}) \]
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