Find all the solutions to
\[\arctan \frac{1}{x} + \arctan \frac{1}{x + 2} = \arctan \frac{4}{x + 3}.\]Enter all the solutions, separated by commas.The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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