Let \(\left\{X_{n}ight\}_{n=1}^{\infty}\) be a sequence of independent random variables where \(X_{n}\) has a Triangular \(\left(\alpha_{n}, \beta_{n}, \gamma_{n}ight)\) distribution for all \(n \in \mathbb{N}\), where \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\), \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\), and \(\left\{\gamma_{n}ight\}_{n=1}^{\infty}\) are sequences of real numbers such that \(\alpha_{n}<\gamma_{n}<\) \(\beta_{n}\) for all \(n \in \mathbb{N}\). Find the necessary properties for the sequences \(\left\{\alpha_{n}ight\}_{n=1}^{\infty}\), \(\left\{\beta_{n}ight\}_{n=1}^{\infty}\), and \(\left\{\gamma_{n}ight\}_{n=1}^{\infty}\) that will ensure that \(\left\{X_{n}ight\}_{n=1}^{\infty}\) is uniformly integrable.