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The exact value of \(\cot\left(\frac{7\pi}{3}\right)\) is \(\frac{\sqrt{3}}{3}\).

Thus, the expression \( g \cdot \cot\left(\frac{7\pi}{3}\right) \) becomes:

\[
g \cdot \frac{\sqrt{3}}{3}
\]

Would you like further clarification or more details on the steps? Here are some related questions you might explore:

1. How is the cotangent function defined in terms of sine and cosine?
2. What is the period of the cotangent function, and why does it affect the angle \( \frac{7\pi}{3} \)?
3. Can we simplify this result further depending on the value of \( g \)?
4. What are the key differences between cotangent, tangent, and their reciprocals?
5. How does this solution change if we use degrees instead of radians?

**Tip:** When dealing with trigonometric functions like cotangent, it's useful to remember their periodic nature to simplify large angles.

Learn how to find the exact value of cot(7π/3) using trigonometric identities and the periodicity of cotangent. This step-by-step solution simplifies the expression to g * (√3 / 3). Suitable for students in Grades 11-12.

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