The C#cim7 is the same as an A7b9 minus the root.


So you are going from Am7, to A7b9, to A7, which will work nicely going in a circle of 5ths context to the next chord.


Also, because diminished 7 chords have no allegiance to any specific key because they are techincally 4 chords at once, you can use them to modulate almost anywhere and justify it.


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