(10) - Outcoming

$\text{E}$ is the midpoint of line segment $\text{DA}$ of trapezium (trapezoid) $\text{ABCD}$ such that $\text{BC} \parallel \text{DA}$ and $\text{AB} = \text{CD}$ , $\widehat{\text{CAB}} = \widehat{\text{BCD}}$ and $\widehat{\text{ECD}} = \widehat{\text{DBC}}$ . Calculate the value of $\left(\dfrac{\text{EC} \cdot \widehat{\text{CDA}}}{\text{BD} \cdot \widehat{\text{BCD}}}\right)^2$ .