` vec u , vec v` and `vec w` are three non-coplanar unit vecrtors and `alpha,beta` and `gamma` are the angles between` vec u` and `vec v , vec v`and `vec w ,a n d vec w` and `vec u ,` respectively, and ` vec x , vec y` and `vec z` are unit vectors along the bisectors of the angles `alpha,betaa n dgamma` , respectively. Prove that `[ vecx xx vec y vec yxx vec z vec zxx vec x]=1/(16)[ vec u vec v vec w]^2sec^2(alpha/2)sec^2(beta/2)sec^2(gamma/2)`.