The product of all possible values of α, for which lim_x → 0((1- cos (α x) cos ((α+1) x) cos ((α+2) x))/(sin^2((α+1) x)))=2, is:

The product of all possible values of $\displaystyle \alpha$, for which $\displaystyle \lim _{x \rightarrow 0}\left(\frac{1-\cos (\alpha x) \cos ((\alpha+1) x) \cos ((\alpha+2) x)}{\sin ^2((\alpha+1) x)}\right)=2$, is: