Given a discrete-time signal

\(x\left( n \right) = \left\{ {\begin{array}{*{20}{c}} { - 1,\;2,\;0,\;2,\;4,\;2}\\ { \uparrow \;} \end{array}} \right\}\)

X(e^jω) is DTFT of x(n).

The value of \(\frac{1}{\pi }\mathop \smallint \nolimits_{ - \pi }^\pi X\left( {{e^{j\omega }}} \right){\sin ^2}\omega \cos \omega \;d\omega = \) ________