Optimize Peripheral Vision

Geometry Level 3

ABDCABDC is a rectangle and PP is a point on the straight line AB\overline{AB}. The lengths of AC\overline{AC} and AB\overline{AB} are 1 and 23\dfrac{2}{\sqrt3}, respectively. Find the maximum value of θ\theta to the nearest integer.

Enter your answer in degrees.

Note: Image drawn not up to scale.

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