  A new definition for the Riemann zeta function for all positive integer
number s > 1 is presented. We discover a most elegant expression and easy
method for calculating the Riemann zeta function for small even integer values.
Through this new reformulation we provide a one-line proof of the value of
zeta(2) and demonstrate that zeta(2s) may be calculated by hand using only the
cotangent function when the magnitude of the integer s is small.
