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Explanation:

Step1: Use the reciprocal identity

Recall that (\csc\theta=\frac{1}{\sin\theta}). So, (\csc\left(\frac{\pi}{3}\right)=\frac{1}{\sin\left(\frac{\pi}{3}\right)}).

Step2: Find the value of (\sin\left(\frac{\pi}{3}\right))

We know that (\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}).

Step3: Calculate (\csc\left(\frac{\pi}{3}\right))

Substitute (\sin\left(\frac{\pi}{3}\right)=\frac{\sqrt{3}}{2}) into (\csc\left(\frac{\pi}{3}\right)=\frac{1}{\sin\left(\frac{\pi}{3}\right)}), we get (\csc\left(\frac{\pi}{3}\right)=\frac{1}{\frac{\sqrt{3}}{2}}). Using the rule (\frac{1}{\frac{a}{b}}=\frac{b}{a}) ((a = \sqrt{3}), (b = 2)), then (\frac{1}{\frac{\sqrt{3}}{2}}=\frac{2}{\sqrt{3}}).

Step4: Rationalize the denominator

Multiply the numerator and denominator by (\sqrt{3}). (\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}}=\frac{2\sqrt{3}}{3}).

Answer:

(\frac{2\sqrt{3}}{3})