In triangle \(ABC\), suppose \(\overline{AB}=10\), \(\overline{AC}=14\) and \(\angle A=105^{\circ}\). If point \(D\) on side \(BC\) satisfies \(\angle BAD=60^{\circ}\) and \(\angle CAD=45^{\circ}\), then what is the value of \(\frac{\overline{BD}^2}{\overline{DC}^2}?\)

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