If a quote is taken from the middle of a sentence, and therefore did not originally start with a capital letter, do we have to capitalize the first letter if we are using the quote at the beginning of a sentence or leave it lower case?
For example,
"Bring that book".
"that" in the above sentence is used as a demonstrative pronoun.
Should we capitalize the 'T' in "that" ?
I would treat the capitalization or non- as part of the exact quote, as it appears in the original.

I don't, however, understand your question, as I cannot see a quote beginning with 'that'.

[I'm of the school that refers to this example of 'that' as a demonstrative adjective.]
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"in" appears twice in your sentence.
In the above sentence do we have to capitalize "i" ?
Yes. But I think you're going to say I'm contradicting myself, perhaps. That's why it's always good to have context.
"We are taught to speak in English in public schools."
Now, in relation to the above sentence if we write:
"in" appears twice in the above sentence.
Do we have to capitalize "i" in "in" ?
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