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Geometry Level 4

Consider the rotation \(T\) of space with \(T(0,0,0)=(0,0,0)\), \(T(6,6,3)=(4,-1,8)\) and \(T(-6,3,6)=(4,8,-1)\). If \((a,b,c)\) is a nonzero point on the axis of rotation, find \(\frac{b+c}{a}\).

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