Cyclic quadrilateral $ABCD$ has side lengths $AB = 2, BC = 3, CD = 5, AD = 4$. 
Find $\sin A \sin B(\cot A/2 + \cot B/2 + \cot C/2 + \cot D/2)^2$. 
Your answer can be written in simplest form as $a/b$. Find $a + b$.

Let's think step by step and output the final answer within \boxed{}.
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