Approximation to $\sum_{n=2}^\infty \frac{1}{n (\ln n)^2}$

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How I can find some good approximation to the series:

$$ \sum_{n=2}^\infty \frac{1}{n (\ln n)^2} $$

The best approximation that I find is 2.056329422629737, but I know it's still a long way off.