Matrix/vector algebra: is this true?

Question

let $z_i$ be a sequence of vectors and $\epsilon_i$ a sequence of scalars, $i = 1, ... , n$.
Does the following hold? $$\frac{1}{n} \left(\left[\sum_{i = 1}^{n}(z_iz_i'\epsilon_i^2)\right]\left[\sum_{i = 1}^{n}(z_iz_i'\epsilon_i^2)'\right] \right)$$ $$= \frac{1}{n} \left(\sum_{i = 1}^{n}(z_iz_i'\epsilon_i^2) + \sum_{i = 1}^{n}\sum_{j = 1, j\neq i}^{n}\epsilon_i\epsilon_jz_iz_j' \right)$$