Find the exact value of the expression. \( \csc \left(\frac{\pi}{3}\right)= \)

The cosecant function is the reciprocal of the sine function. We know that \( \sin \left( \frac{\pi}{3} \right) = \frac{\sqrt{3}}{2} \). Thus, to find \( \csc \left( \frac{\pi}{3} \right) \), we take the reciprocal of \( \sin \left( \frac{\pi}{3} \right) \): \[ \csc \left( \frac{\pi}{3} \right) = \frac{1}{\sin \left( \frac{\pi}{3} \right)} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} \] To make it neater, we can rationalize the denominator: \[ \csc \left( \frac{\pi}{3} \right) = \frac{2 \cdot \sqrt{3}}{3} \] So, the exact value of \( \csc \left( \frac{\pi}{3} \right) \) is \( \frac{2 \sqrt{3}}{3} \).