Sum of Squares

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If \(4cos \frac{\pi}{5} + cot \frac{\pi}{24} \) = \( \sqrt{n_1} + \sqrt{n_2} + \sqrt{n_3} + \sqrt{n_4} + \sqrt{n_5} + \sqrt{n_6}\),

find \(\sum_{i=1}^6 n^{2}_i\).

\(Note\) : \(All\) \(n_i\)\('s\) \(are\) \(natural\) \(numbers.\)

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