Sum of last eight coefficient are 

${\rm{S}} = {\,^{15}}{{\rm{C}}_8} + {\,^{15}}{{\rm{C}}_9} + {\,^{15}}{{\rm{C}}_{10}} +  \ldots . + {\,^{15}}{{\rm{C}}_{15}}$      ….$(1)$

${\rm{S}} = {\,^{15}}{{\rm{C}}_7} + {\,^{15}}{{\rm{C}}_6} + {\,^{15}}{{\rm{C}}_5} +  \ldots . + {\,^{15}}{{\rm{C}}_0}$           …$(2)$

$\left\{ {{\rm{ We know that}}{{\rm{ }}^{15}}{{\rm{C}}_8} = {\,^{15}}{{\rm{C}}_7}} \right\}$

$e q^{n}(1)+(2)$

$2{\rm{S}} = {\,^{15}}{{\rm{C}}_0} + {\,^{15}}{{\rm{C}}_1} + {\,^{15}}{{\rm{C}}_2} +  \ldots .{\,^{15}}{{\rm{C}}_{15}}$

$\Rightarrow 2 S=2^{15} \Rightarrow S=2^{14}$