Find the value of `4 tan^(-1).(1)/(5) - tan^(-1).(1)/(70) + tan^(-1).(1)/(99)`

Explanation

To solve the problem \( 4 \tan^{-1}\left(\frac{1}{5}\right) - \tan^{-1}\left(\frac{1}{70}\right) + \tan^{-1}\left(\frac{1}{99}\right) \), we can use the properties of inverse tangent functions. Let's break it down step by step.

### Step 1: Use the double angle formula
We can express \( 4 \tan^{-1}\left(\frac{1}{5}\right) \) as:
\[ 4 \tan^{-1}\left(\frac{1}{5}\right) = 2 \cdot 2 \tan^{-1}\left(\frac{1}{5}\right) \]
Using the formula \( 2 \tan^{-1}(x) = \tan^{-1}\left(\frac{2x}{1-x^2}\right) \):
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