In the figure above, \(\triangle ABC\) has \(\angle A = 45^\circ \) and \(\angle B = 30^\circ \). A line \(DE\) with \(D\) on \(AB\) and \(\angle ADE = 60^\circ \), divides \(\triangle ABC \) into two pieces of equal area.

What is the ratio of \(\dfrac{AD}{AB} \)?

Give your answer to 3 decimal places.

**Note**: The figure above may not be accurate, perhaps \(E\) is on \(CB\) instead of \(AC\).

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