Uniform Distribution Modulo 1

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Let

$x_1 = \sqrt2$ mod $1$

$x_2 = 2x_1$ mod $1$

$x_3 = 2x_2$ mod $1$

continue the process

How to prove the sequence {$x_n$} is uniformly distributed modulo 1

my friend tell me that the question can be solved by Calculus

but I still have no idea