Write the value of `sin^(2)theta cos^(2)theta(1+tan^(2)theta)(1+cot^(2)theta).`

Explanation

To solve the expression \( \sin^2 \theta \cos^2 \theta (1 + \tan^2 \theta)(1 + \cot^2 \theta) \), we will use some trigonometric identities.

### Step-by-Step Solution:

1. **Identify the identities**:
We know the following trigonometric identities:
- \( 1 + \tan^2 \theta = \sec^2 \theta \)
- \( 1 + \cot^2 \theta = \csc^2 \theta \)

2. **Rewrite the expression**:
Using the identities, we can rewrite the expression:
\[ (1 + \tan^2 \theta) = \sec^2 \theta \quad \text{and} \quad (1 + \cot^2 \theta) = \csc^2 \theta \]
Therefore, the expression becomes:
\[ \sin^2 \theta \cos^2 \theta \cdot \sec^2 \theta \cdot \csc^2 \theta \]

3. **Substitute sec and csc**:
Recall that:
\[ \sec \theta = \frac{1}{\cos \theta} \quad \text{and} \quad \csc \theta = \frac{1}{\sin \theta} \]
Thus:
\[ \sec^2 \theta = \frac{1}{\cos^2 \theta} \quad \text{and} \quad \csc^2 \theta = \frac{1}{\sin^2 \theta} \]
Substituting these into the expression gives:
\[ \sin^2 \theta \cos^2 \theta \cdot \frac{1}{\cos^2 \theta} \cdot \frac{1}{\sin^2 \theta} \]

4. **Simplify the expression**:
Now, we can simplify the expression:
\[ \sin^2 \theta \cos^2 \theta \cdot \frac{1}{\cos^2 \theta \sin^2 \theta} = \frac{\sin^2 \theta \cos^2 \theta}{\sin^2 \theta \cos^2 \theta} = 1 \]

5. **Final result**:
Therefore, the value of the expression \( \sin^2 \theta \cos^2 \theta (1 + \tan^2 \theta)(1 + \cot^2 \theta) \) is:
\[ \boxed{1} \]