It looks like you're trying to express a relationship or equation involving trigonometric functions, specifically involving cotangent and tangent. However, the equation you provided seems a bit unclear due to formatting. Let’s clarify the expression step by step.

### Given:
You seem to have two expressions:
1. \( Y = \frac{\cot(2x - \frac{\pi}{3})}{1 + \tan(xy)} \)
2. \( y = \frac{\cot(2x - \frac{\pi}{3})}{1 + \tan(x)} \)

### Clarifying the Terms
1. **Cotangent Function**: \( \cot(z) = \frac{1}{\tan(z)} \)
2. **Tangent Function**: \( \tan(z) = \frac{\sin(z)}{\cos(z)} \)

### Interpretation:
It's important to understand how these functions behave and how they can be manipulated. If we are trying to relate \( Y \) and \( y \) or find conditions under which they behave similarly or are equal, further analysis would be needed with specific values or conditions.

### Further Exploration:
If you're looking to solve for \( y \) in terms of \( Y \), or find a relationship between the two, we may need additional context or constraints.

If you clarify the objective (e.g., solving for \( y \), demonstrating a property, or needing a specific derivation), I would be happy to assist further!