I want to calculate this limit for quite some days now and I have made almost no progress whatsoever.

(limit of sin(2^n) as n-> infinity, neN ) I suspect either lim(sin(2^n)) = 0 or it is non-existing.

Thus fur I have used numerous trigonometry properties resulting to nowhere,

also I tried to prove it converges to 0 but turned out my calculations lead it diverging which is impossible.

I can't seem to find a proper way of calculating/solving this other than an informal theoretical way.

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