  Finite trigonometric sums occur in various branches of physics, mathematics,
and their applications. These sums may contain various powers of one or more
trigonometric functions. Sums with one trigonometric function are known,
however sums with products of trigonometric functions can get complicated and
may not have a simple expressions in a number of cases. Some of these sums have
interesting properties and can have amazingly simple value. However, only some
of them are available in literature. We obtain a number of such sums using
method of residues.
