Arctan in 2015

Geometry Level 4

\[ \tan(\arctan 2 + \arctan 0 +\arctan 1 + \arctan 5 - \arctan 2015) \]

If the value of expression above can be stated as \(-\frac{p}{q},\) where \(p\) and \(q\) are relatively prime positive integers. Find \(p + q.\)