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The problem asks to calculate \( \sin(\arctan(\sqrt{3})) \).

### Step-by-Step Solution:

1. **Understand the Function:**
   - \( \arctan(\sqrt{3}) \) gives the angle \( \theta \) such that \( \tan(\theta) = \sqrt{3} \).

2. **Determine the Angle \( \theta \):**
   - \( \tan(\theta) = \sqrt{3} \) corresponds to the standard angle \( \theta = \frac{\pi}{3} \) (or 60°) because \( \tan\left(\frac{\pi}{3}\right) = \sqrt{3} \).

3. **Calculate \( \sin(\theta) \):**
   - Now, you need to find \( \sin\left(\frac{\pi}{3}\right) \).
   - \( \sin\left(\frac{\pi}{3}\right) = \frac{\sqrt{3}}{2} \).

### Final Answer:
\[
\sin(\arctan(\sqrt{3})) = \frac{\sqrt{3}}{2}
\]

Would you like more details or have any questions about this solution?

Here are some related questions that might interest you:
1. What is the geometric interpretation of \( \arctan(x) \)?
2. How do you find the sine of an angle using a right triangle?
3. What is the relationship between \( \arctan \) and \( \sin \) for other values?
4. How would you solve \( \cos(\arctan(x)) \) instead?
5. What is the general formula for \( \sin(\arctan(x)) \) in terms of \( x \)?

**Tip:** Always remember the standard angles and their trigonometric values; they come in handy for problems like this!

Explore a detailed step-by-step solution to calculate sin(arctan(sqrt(3))). This problem involves trigonometric identities and inverse trigonometric functions, focusing on finding the sine of an angle derived from the arctangent function. Suitable for advanced high school students.

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