To find the exact value of $\sec \left( \frac{\pi}{3} \right)$, we can use the trigonometric identity for secant:

$\sec \theta = \frac{1}{\cos \theta}$

For $\theta = \frac{\pi}{3}$, we need to know the value of $\cos \left( \frac{\pi}{3} \right)$. From the standard trigonometric table, we know that:

$\cos \left( \frac{\pi}{3} \right) = \frac{1}{2}$

Now, apply the secant formula:

$\sec \left( \frac{\pi}{3} \right) = \frac{1}{\cos \left( \frac{\pi}{3} \right)} = \frac{1}{\frac{1}{2}} = 2$

So, the exact value of $\sec \left( \frac{\pi}{3} \right)$ is $2$.

Would you like more details or have any questions about this? Here are 5 related questions to explore:

1. What is the exact value of $\sec \left( \frac{\pi}{6} \right)$?
2. How do you calculate $\sec \theta$ for an angle not on the unit circle?
3. Can you express $\sec \theta$ in terms of $\sin \theta$?
4. What is the relationship between secant and cosine functions?
5. How would you solve $\sec \theta = 2$ for $\theta$?

Tip: For angles on the unit circle, always recall their basic sine and cosine values to quickly find secant, cosecant, tangent, and cotangent.