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Geometry Level 5

Consider \(\Delta ABC\) having \(I\) as its incenter and \(I_1,I_2,I_3\) as its excenters opposite to vertices \(A,B,C\) respectively.If \(\Delta ABC\) has a unit circumradius , find the value of :

\[\Large\displaystyle\sum_{cyc\{1,2,3\}} (II_1^2 + I_2I_3^2)\]

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