The expression $\csc(\theta) \cdot \cos(\theta)$ can be simplified as follows:

Recall that:

$\csc(\theta) = \frac{1}{\sin(\theta)}$

Substitute this into the expression:

$\frac{1}{\sin(\theta)} \cdot \cos(\theta)$

This simplifies to:

$\frac{\cos(\theta)}{\sin(\theta)}$

Now, recall that $\frac{\cos(\theta)}{\sin(\theta)}$ is equal to $\cot(\theta)$ (cotangent of $\theta$).

So, the simplified expression is:

$\boxed{\cot(\theta)}$

Let me know if you'd like further details on this or have any other questions!

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Here are 5 related questions to deepen your understanding:

1. How do you derive the identity for $\cot(\theta)$?
2. What is the relationship between $\cot(\theta)$ and other trigonometric functions?
3. How can you express $\sec(\theta) \cdot \sin(\theta)$ in terms of a single trig function?
4. Can $\cot(\theta)$ ever be undefined, and under what conditions?
5. How does $\csc(\theta) \cdot \sin(\theta)$ simplify?

Tip: Memorizing the core trigonometric identities like $\csc(\theta) = \frac{1}{\sin(\theta)}$ and $\cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)}$ will help you simplify many complex expressions faster.