Inspired by Otto Bretscher

Evaluate

$\large{\left\lfloor \sum _{ n=1 }^{ 2015 }{ \left( lcm{ \left( 2015,n \right) \tan { \left( \frac { 2\pi n }{ 2015 } \right) } } \right) } \right\rfloor }$

This question inspired from this question by Otto Sir who is loved by many students at Brilliant and at Colby College

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