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.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\sqrt{5}
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.
train