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It's pronounced [c̟ɕiʑimete], although in careful speech it would probably be [c̟ɕiɟʑimete]―there's no contrast between [ʑi] and [ɟʑi] in Modern Japanese, so the word will be understood either way.

For the pronunciation of ち and ぢ, see section 4.3 "Affricates" in Vance's The Sounds of Japanese (2008), starting on page 82. Most of this section is available online at Google Books.

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