The given expression is:

$\cot\left(\frac{\pi}{2} - \theta\right) \cdot \csc(\theta)$

Using the co-function identity for cotangent:

$\cot\left(\frac{\pi}{2} - \theta\right) = \tan(\theta)$

This simplifies the expression to:

$\tan(\theta) \cdot \csc(\theta)$

Now, we know that $\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ and $\csc(\theta) = \frac{1}{\sin(\theta)}$. Substituting these into the expression gives:

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

Thus, the expression simplifies to:

$\sec(\theta)$

So the final answer is:

$\sec(\theta)$

Do you want more details or have any questions? Here are 5 related questions:

1. What is the co-function identity for $\sin\left(\frac{\pi}{2} - \theta\right)$?
2. How does the identity for $\tan(\theta)$ relate to $\cot(\theta)$?
3. What is the difference between secant and cosine in terms of their definitions?
4. How would the expression change if it were $\cot(\theta) \cdot \csc\left(\frac{\pi}{2} - \theta\right)$?
5. Can you derive the identity for $\sec(\theta)$ using right triangles?

Tip: Understanding co-function identities (like $\sin\left(\frac{\pi}{2} - \theta\right) = \cos(\theta)$) helps in simplifying many trigonometric expressions!