Step 1 :The given expression is in the form of \(\frac{\tan a + \tan b}{1 - \tan a \tan b}\), which is equivalent to \(\tan(a+b)\). So, we need to find the sum of the angles \(\frac{3\pi}{5}\) and \(\frac{\pi}{6}\).
Step 2 :Let a = \(\frac{\pi}{6}\) and b = \(\frac{3\pi}{5}\)
Step 3 :Calculate the sum of the angles a and b, which is \(\frac{23\pi}{30}\)
Step 4 :Final Answer: The expression is equivalent to \(\tan \frac{23 \pi}{30}\), so the correct answer is \(\boxed{A. \tan \frac{23 \pi}{30}}\)