Convergence/Divergence of the series $\sum_{n=1}^{+\infty}(3^{1/n^2} -1) \csc^2n$

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$\sum_{n=1}^{+\infty}(3^{1/n^2} -1) \csc^2n$

It's obviously a positive series and the parts of $\csc^2n $ tells me it might be divergent. But I have no idea how to prove it. Any one can offer some help or hints?