Taylor, Maclaurin, & Power series challenge

Let $~g\left( x \right)=\sin \left( 2x-\dfrac{\pi }{2} \right)~$space, g, left parenthesis, x, right parenthesis, equals, sine, left parenthesis, 2, x, minus, start fraction, pi, divided by, 2, end fraction, right parenthesis, space and let $~{{T}_{3}}\left( x \right)~$space, T, start subscript, 3, end subscript, left parenthesis, x, right parenthesis, space be the third-degree Taylor polynomial for $~g~$space, g, space centered at $~x=0\,$space, x, equals, 0. Determine the sum of the coefficients of $~T_3\,$space, T, start subscript, 3, end subscript.