If `tan^(-1)(1/(1+1. 2))+tan^(-1)(1/(1+2. 3))+....
+tan^(-1)(1/(1+n.(n+1)))=tan^(-1)theta,` then find the value of `thetadot`

Explanation

To solve the problem, we need to evaluate the sum of the series involving the inverse tangent function and express it in terms of \( \theta \).

### Step 1: Write the series in terms of inverse tangent
The given series is:
\[ S = \tan^{-1}\left(\frac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\frac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\left(\frac{1}{1 + n(n+1)}\right) \]

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