Let $D$ be a point on the side $[BC]$ of $\triangle ABC$ such that $|BD|=2$ and $|DC|=6$. If $|AB|=4$ and $m(\widehat{ACB})=20^\circ$, then what is the value of $m(\widehat{BAD})$ in degrees?

Let's think step by step and output the final answer within \boxed{}.
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