Absolutely geometric

In triangle $PQR$ , the respective length of the sides $PQ$ and $PR$ are denoted by $u$ and $v$ while the length of the median $PS$ is denoted by $w$ . It is known that $w$ is the geometric mean of $u$ and $v$ , and $\angle QPR = 60$ .

The value of $|\cos(\angle PQR) - \cos(\angle QRP) | = \dfrac{a}{b\sqrt{c}}$ , where $|x|$ denotes the absolute value of $x$ .

Then find the value of $a+b+c$