Finding the sum of a series of natural logs

Finding the sum of a series of natural logs

Heyya,
So I have this problem for midterm reviews:
$$\sum_{n=2}^\infty \ln\left(1-\frac{1}{n^2}\right)=\text{ ?}$$
I know that you can find the series form of a natural log, as shown here:
$$\ln\left(1-\frac{1}{n^2}\right)=-\sum_{k=2}^\infty
\left(\frac{1}{n^{4k}}\right)\left(\frac{1}{2k}\right) $$
But the above doesn't seem to help very much since it results in two
summation notations mushed together. Is there a somewhat nontedious way to
go about this? Thanks! All help appreciated.