Trigonometric Lengths

Geometry Level 3

In triangle \( ABC\), \(\angle ACB = 90^\circ \). \(A, D, E,\) and \(B\) are consecutive points on \(AB\) such that \(\overline{AD}=\overline{DE}=\overline{EB}\). If there exists \( \theta\) such that \( \overline{CD} = 5 \cos \theta\) and \(\overline{CE} = 5 \sin \theta \), what is \(\overline{AB}^2?\)

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