3030^\circ Is Always Good

Geometry Level 4

AB=CD=1AB = CD = 1, mABC=90m\angle ABC = 90^\circ, mCBD=30m\angle CBD = 30^\circ. AA, CC, and DD, are collinear. ACAC can be represented in the simplest form as a1/ba^{1/b}, where aa and bb are positive integers such that aa is minimized. Find a+ba + b.

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