Find the exact value of the expressi \( \tan \left(\arccos \left(\frac{\sqrt{3}}{2}\right)\right)=\square \) (Type an exact answer, using \( \pi \) and

Find the value of \( \tan(\arccos(\frac{\sqrt{3}}{2})) \). Calculate the value by following steps: - step0: Calculate: \(\tan\left(\arccos\left(\frac{\sqrt{3}}{2}\right)\right)\) - step1: Rewrite the expression: \(\frac{\sqrt{1-\left(\frac{\sqrt{3}}{2}\right)^{2}}}{\frac{\sqrt{3}}{2}}\) - step2: Subtract the numbers: \(\frac{\sqrt{\frac{1}{4}}}{\frac{\sqrt{3}}{2}}\) - step3: Simplify the root: \(\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}\) - step4: Multiply by the reciprocal: \(\frac{1}{2}\times \frac{2}{\sqrt{3}}\) - step5: Reduce the numbers: \(1\times \frac{1}{\sqrt{3}}\) - step6: Multiply: \(\frac{1}{\sqrt{3}}\) - step7: Multiply by the Conjugate: \(\frac{\sqrt{3}}{\sqrt{3}\times \sqrt{3}}\) - step8: Multiply the numbers: \(\frac{\sqrt{3}}{3}\) The exact value of \( \tan \left(\arccos \left(\frac{\sqrt{3}}{2}\right)\right) \) is \( \frac{\sqrt{3}}{3} \).