How to pronounce Catherine De' Medici?

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Catherine De' Medici is pronounced as

kaa·tai·ree·nai  deh  mai·dee·chee  

k	is pronounced as		k	in key
aa	is pronounced as		aa	in car
t	is pronounced as		t	in to
ai	is pronounced as		ai	in pain
r	is pronounced as		r	in rat
ee	is pronounced as		ee	in see
n	is pronounced as		n	in no
d	is pronounced as		d	in do
ch	is pronounced as		ch	in chin