\(30^\circ\) Is Always Good

Geometry Level 4

\(AB = CD = 1\), \(m\angle ABC = 90^\circ\), \(m\angle CBD = 30^\circ\). \(A\), \(C\), and \(D\), are collinear. \(AC\) can be represented in the simplest form as \(a^{1/b}\), where \(a\) and \(b\) are positive integers such that \(a\) is minimized. Find \(a + b\).

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