This may not be that bad, but give it a go for those who wish.
Let's see what interesting methods are come up with.
We know that
so then I think what you can do is this
so we have
by PFD and use of a riemann zeta table =D
NOTE: what I mean by PFD was that after I decomposed it it gave a telescoping series and a riemann zeta function, which came out to be , the latter riemann zeta was gotten using the CRC table of values