I need to calculate the variance of the sample variance and thus prove
that it equals to (2theta^4)/(n-1)

The webbed version of the Concise Encyclopedia of Mathematics CD-ROM
by Eric W. Weisstein:

http://hades.ph.tn.tudelft.nl/Internal/PHServices/Documentation/MathWorld/math/math/g/g084.htm

Scroll down the page to (49) and (50), which derives the result you
are looking for.

I would add that if you are looking for Mathworld, the correct url is:

http://mathworld.wolfram.com/GaussianDistribution.html

The one nauster-ga gives is a (unauthorized) mirror of Mathworld that
was created when Eric Weisstein was having legal problems with the
publishers of the encyclopedia. But now that the legal problems are
somewhat resolved, the main site is back in operation.

Anyway both links have the solution you are looking for - I think
that's as good as you'll get unless an enthusiast decides to give you
a >$2 answer :)

Here is a link to a formula of variance of sample variance
Please search for "variance of the sample variance"in this web page.

http://mathworld.wolfram.com/GaussianDistribution.html