Some Right Triangles

Geometry Level 2

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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