If , then the value of must…

MATHEMATICS · Subjective · A Level · Mathematics · Trigonometry · Trigonometry

Problem

4 \cos 36^\circ + \cot \left( 7 \frac{1}{2}^\circ \right) = \sqrt{n_1} + \sqrt{n_2} + \sqrt{n_3} + \sqrt{n_4} + \sqrt{n_5} + \sqrt{n_6}

, then the value of

\sum_{i=1}^{6} n_i^2

must be