This is an oxymoron.
Shouting and quietly used side by side, two words with opposite meaning.
This is really interesting.
From the contextual standpoint, it makes sense literally to shout in a quiet way; which is why "he was shouting in a quiet way ".
I would not know how to classify the expression, whether he is being polite or not. I guess it depends on the receiver of the action. Some folks love the quiet and calm so much, anything else is being disrespectful.
So, shout quietly at your own risk.
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