Triangle \(ABC\) has \(\angle ABC = 90 ^\circ\) and \(\angle CAB = 30^\circ\). Triangle \(DAC\) has \(\angle DAC = 90^\circ\) and \(\angle CDA = 30^\circ\). Similarly, triangle \(EDC\) has \(\angle EDC = 90^\circ\) and \(\angle CED = 30^\circ\). If \(EC = 136\), what is the value of \(BC\)?

**Details and assumptions**

For simplicity, you may assume that the triangles do not overlap. However, this assumption isn't necessary.

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