Some fascinating series and their sums

TL;DR

This paper introduces new, elegant finite series identities involving trigonometric sums that are not found in existing literature or derivable by standard computational tools.

Contribution

The paper presents novel finite series identities involving trigonometric sums that are not documented in current mathematical references or derivable by common software.

Findings

New trigonometric series identities discovered

Identities are not present in existing literature or computational tools

Results contribute to the theory of finite series and trigonometry

Abstract

In this paper we present some interesting results involving summation of series in particular trigonometric ones. We failed to locate these results in existing literature or in the web like MathWorld (http://mathworld.wolfram.com/) nor could we derive them using software for analytical computation like Maple. The identities are beautiful and involve finite series.