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Geometry Level 5

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 \(T(3,9,12)=(a,b,c)\), find \(a+b+c\).

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