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 $$\frac{b+c}{a}$$.