\(ABCD\) is a square. Point \(E\), located on the opposite side of line \(CD\) as compared to points \(A\) and \(B\), satisfies \( \angle DEA = \angle AEC = \frac{1}{2} \angle EAD \). What is the measure of \( \angle ECD\)?

**Details and assumptions**

Points \(X\) and \(Y\) are on **opposite sides of line \(MN\)** if the line segment \(XY\) intersects the line \(MN\).

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