x[n] has a Fourier transform \({\rm{X}}\left( {{e^{j\omega }}} \right){\rm{}}\) with

i) x[n] = 0    n > 0

ii) x[0] > 0

iii) \({\rm{Imaginary}}\left\{ {{\rm{X}}\left( {{e^{j\omega }}} \right){\rm{}}} \right\}{\rm{}} = {\rm{sin\omega }}-{\rm{sin}}2{\rm{\omega }}\)

iv) \(\mathop \smallint \limits_{ - \pi }^\pi {\left| {X\left( {{e^{j\omega }}} \right)} \right|^2}d\omega = 6\pi\)

Then \(\mathop \sum \limits_{n = - \infty }^\infty x\left[ n \right]\) is ___________.