Prove that: `tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={ when 0

Explanation

To prove that

\[ \tan^{-1}\left(\frac{1}{2\tan 2A}\right) + \tan^{-1}(\cot A) + \tan^{-1}(\cot^3 A) = \pi \]

for \(0 < A < \frac{\pi}{4}\), we will follow these steps:

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