Let \( E, F, G, H \) be 4 distinct points inside square \( A B C D \) whose area is 1 square uni...

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Let \( E, F, G, H \) be 4 distinct points inside square \( A B C D \) whose area is 1 square units such that \( \angle E D C=\angle E C D=\angle H D A= \) \( \angle H A D=\angle G A B=\angle G B A=\angle F B C=\angle F C B=15^{\circ} \)
(i) If \( \angle A E B=\frac{\pi}{k} \); then find \( k \)
(ii) Find the radius of circle circumscribing the \( \triangle A H D \)
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