It might also be worth mentioning that you can buy matt screen protectors (confusingly often referred to as 'anti-glare') that significantly cut down reflections, albeit at some small cost to clarity. I have one on my iPad, and there's a slightly 'granular' texture to the screen - a price I'm happy to pay for the benefits it brings to me; you may feel differently of course, but the option is there if needed.
Cheers, Pete
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