Angle Between Diagonals?

Geometry Level 4

Find the acute angle \(\theta\) between the diagonals of a rectangle with perimeter \(2p\) and area \(\dfrac{3}{16}p^{2}\).

If \(\theta\) \(=\) \(a\) \(\tan^{-1} \left(\dfrac{b}{c} \right)\) , where \(a , b , c\) are coprime positive integers, then enter the value of \(a + b + c\) .

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