Contour integration, cos(z)sin(z)

Question

Evaluate \begin{equation*} \int_{\Gamma}\cos(z)\sin(z)dz,~\Gamma:\gamma(t):=\pi t+(1-t)i,~0\leq t\leq 1. \end{equation*}

I think I should do it using this \begin{equation*} \int_{\gamma}f(z)dz=\int^b_a f(\gamma(t))\gamma'(t)dt \end{equation*}

but when I sub in gamma the integral seems very difficult? Is there an easier way to do this?

Thanks