# Tan on the floor!

Level pending

A positive integer $$n \in S$$, the set of tanny integers, if and only if for some value of $$\theta \in (0,\frac{\pi}{2})$$, $$\lfloor \tan^2{\theta} \rfloor + \tan{\theta} = n$$. When the elements of $$S$$ are arranged in increasing order, let $$N_{T_{2014}}$$ denote the $$2014$$th tanny integer. Find the last three digits of $$N_{T_{2014}}$$.

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