Direction : Consider the following for the items that follow :  

Let (8 + 3√7) ²⁰  = U + V and (8 - 3√7) ²⁰  = W, where U is an integer and 0 < V < 1.

What is the coefficient of $x^{10}$ in the expansion of $(1-x^2)^{20}\left(2-x^2-\frac{1}{x^2}\right)^{-5}$?

If the 4th term in the expansion of $\left(mx + \frac{1}{x}\right)^n$ is $\frac{5}{2}$, then what is the value of $mn$?