Inverse Trigonometric Functions

Let \(x = \sin (2{\tan ^{ - 1}}\alpha )\) and \(y = \sin \left( {{1 \over 2}{{\tan }^{ - 1}}{4 \over 3}} \right)\). If \(S = \{ a \in R:{y^2} = 1 - x\}\), then \(\sum\limits_{\alpha \in S}^{} {16{\alpha ^3}}\) is equal to _______________.