The set $\{x\in\mathbb R\mid x>0,(1+x^2)\tan2x=x\}$ is countably infinite

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The set $\{x\in\mathbb R\mid x>0,(1+x^2)\tan2x=x\}$ is

  1. Empty

  2. Finite

  3. Countably infinite

  4. Uncountable

I have plotted the graph and see that the required set is countably infinite. How to prove this fact?