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To solve this problem, let's analyze the expression given:

**Expression to simplify**:  
\[
\sin^2 \theta (1 + \cot^2 \theta)
\]

### Step-by-Step Solution

1. **Rewrite \(\cot^2 \theta\) in terms of sine and cosine:**
   \[
   \cot \theta = \frac{\cos \theta}{\sin \theta}
   \]
   So,
   \[
   \cot^2 \theta = \frac{\cos^2 \theta}{\sin^2 \theta}
   \]

2. **Substitute \(\cot^2 \theta\) into the expression:**
   \[
   \sin^2 \theta \left(1 + \frac{\cos^2 \theta}{\sin^2 \theta}\right)
   \]

3. **Simplify the expression inside the parentheses:**
   \[
   1 + \frac{\cos^2 \theta}{\sin^2 \theta} = \frac{\sin^2 \theta + \cos^2 \theta}{\sin^2 \theta}
   \]

   Using the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\), we get:
   \[
   1 + \frac{\cos^2 \theta}{\sin^2 \theta} = \frac{1}{\sin^2 \theta}
   \]

4. **Rewrite the entire expression:**
   \[
   \sin^2 \theta \cdot \frac{1}{\sin^2 \theta}
   \]

5. **Simplify by canceling \(\sin^2 \theta\):**
   \[
   \sin^2 \theta \cdot \frac{1}{\sin^2 \theta} = 1
   \]

### Conclusion
The expression simplifies to \(1\).

### Answer
The correct answer is:
- **C. \(1\)**

Would you like further details on any specific steps? 

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Here are five questions for practice:
1. What is the Pythagorean identity involving \(\sin^2 \theta\) and \(\cos^2 \theta\)?
2. How can you express \(\cot^2 \theta\) in terms of \(\sin \theta\) and \(\cos \theta\)?
3. Why does \(\sin^2 \theta \cdot \frac{1}{\sin^2 \theta}\) simplify to \(1\)?
4. What other trigonometric identities can help simplify complex expressions?
5. How would the solution change if the original expression were \(\sin^2 \theta (1 - \cot^2 \theta)\)?

#### Tip:
When simplifying trigonometric expressions, look for identities that can help convert terms into sine and cosine, as this often makes simplification easier.

Write the expression \( \sin^2 \theta (1 + \cot^2 \theta) \) in terms of sine and cosine, and simplify so that no quotients appear in the final expression.

Step-by-step solution for simplifying the trigonometric expression \( \sin^2 \theta (1 + \cot^2 \theta) \) by rewriting in terms of sine and cosine, applying trigonometric identities, and ensuring no quotients in the final answer. Suitable for high school students studying trigonometry.

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