For a portfolio-wide profit/loss variable $X= \sum_{i=1}^{n}w_iX_i$ the value-at-risk of $X$ at confidence level $\alpha$ (usually close to 1) is defined as the $\alpha$-quantile of $-X$:
\begin{equation} VaR_{\alpha}(X) = q_{\alpha}(-X) \end{equation}
The formula for the Euler VaR-contributions reads \begin{equation} VaR_{\alpha}(X) = \sum_{j=1}^{n} w_iVaR_{\alpha}(X_i | X) \end{equation} where for $i=1, 2, \cdots, n$, we have that \begin{equation} VaR_{\alpha}(X_i| X) = -\mathbb{E}[X_i | X= -VaR_{\alpha}(X) ] \end{equation} Using the linear approximation, it can be shown that
\begin{equation} VaR_{\alpha}(X_i| X) \approx \frac{Cov(X_i, X)}{Var(X)}\Big(VaR_{\alpha}(X)+ \mathbb{E}(X)\Big)- \mathbb{E}(X_i) \end{equation}
My question is, how we can come up with the above relation?
Thank you in advance.