Can't use Thales' theorem!

Geometry Level 4

Let a circle with radius 1 have centre \(O\), and let \(AB\) be its diameter. \(C\), \(D\) and \(E\) are collinear points in that order such that \(C\) is on \(AB\) extended closer to \(A\), \(D\) and \(E\) are on the circle and \(BE=ED=DC\). If the value of \(\cos \angle EOB\) can be represented as \(\dfrac {a}{b}\), where \(a\) is an integer, \(b\) is a positive integer and both are coprime, find the value of \(a+b\).

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