How can we prove that
$$\frac{\eta^{14}(q^4)}{\eta^{4}(q^8)}=4\eta^4(q^2)\eta^2(q^4)\eta^4(q^8)+\eta^4(q)\eta^2(q^2)\eta^4(q^4) \ ?$$

Here, $\eta(q)$ is the [Dedekind Eta Function](http://en.wikipedia.org/wiki/Dedekind_eta_function), which is defined by

$$\eta(q)=q^{1/24}\prod\_{n=1}^\infty \left(1-q^{n} \right) $$

I looked up some identities of Dedekind Eta Function in the hope of simplifying the right hand expression but I failed. I would be grateful if any one could suggest a proof of this identity.

**Source**

I came across this identity in a paper. They refer to Entry $t\_{8,12,48}$ and $t\_{8,18,60a}$ of [Dedekind eta function product identities](http://eta.math.georgetown.edu/). Unfortunately, I was unable to find these entries on that site.