# Strange cyclic quadrilateral

**Geometry**Level 5

Let the equation \(x^4-24x^3+201x^2-698x+844=0\) has roots \(a\), \(b\), \(c\) and \(d\).

If the value of \(\sin \alpha + \sin \theta + \sin \gamma + \sin \beta\) can be written as \(\dfrac{m}{\sqrt{n}}\), where \(m\) and \(n\) are positive integers with \(n\) -square-free, find \(m+n\).

**Note:** Such quadrilateral indeed exists, the image is up to scale.