Writing 1/2 as a sum of inverse squares

There are several ways to write the number 1/2 as a sum of inverse squares using distinct integers.

For instance, the numbers {$2,3,4,5,7,12,15,20,28,35$} can be used:

$$ \frac{1}{2} = \frac{1}{2^2} + \frac{1}{3^2} + \frac{1}{4^2} + \frac{1}{5^2} + \frac{1}{7^2}+\frac{1}{12^2} + \frac{1}{15^2} + \frac{1}{20^2} + \frac{1}{28^2} + \frac{1}{35^2} $$

In fact, only using integers between $2$ and $45$ inclusive, there are exactly three ways to do it, the remaining two being: {$2,3,4,6,7,9,10,20,28,35,36,45$} and {$2,3,4,6,7,9,12,15,28,30,35,36,45$}.

How many ways are there to write the number 1/2 as a sum of inverse squares using distinct integers between $2$ and $80$ inclusive?