# Tan on the floor!

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 \(N_{T_{2014}}\).