Evaluate the product of terms involving squares from 2 to 15.

What is the value of the product:
$\prod_{n=2}^{15} \left(1 - \frac{1}{n^2}\right)?$
This product can be expressed as:
$(1 - \frac{1}{4})(1 - \frac{1}{9})(1 - \frac{1}{16}) \cdots (1 - \frac{1}{225})$
where the terms correspond to the squares of the integers from 2 to 15.