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The coordination sphere is the sphere around the molecules and ions attached to the transition metal atom. The ligands need to be in the sphere because ligands are the ions attached to the transition metals. Anything within the "" is inside the coordination sphere
Ligands directly attached to the central ion make up the first coordination sphere, and the second coordination sphere consists of atoms/molecules attached to those in the first coordination sphere. Everything inside the brackets will be inside the coordination sphere.
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