50 follower problem

Calculus Level 3

\[\lim_{x\to \infty} x^2 \sqrt {\bigg( 1-cos\frac{1}{x} \bigg) \sqrt {\bigg( 1-cos\frac{1}{x} \bigg) \sqrt{\bigg( 1-cos\frac{1}{x} \bigg) \sqrt {... }}}} =? \]

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