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sorting list of roots af a transcendental function


Dear group,

for calculating a model i need values for x which are given by the 
transcendental function Cot[x] == x/a - a/(4*x). a is a parameter 0<a<200.
i obtained the roots with Table and FindRoot:
Table[FindRoot[Cot[x] == x/a - a/(4*x), {x, i}], {i, 1, 50}]]

I have two questions:
1. Is there a better way to do this?
2. How can i construct a list, where the values for x, which appear 
multiple are dropped?

Thanks!


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