将\((x^{2}+x+1)^{n}\)展开，当\(n=0\)，\(1\)，\(2\)，\(3\)，\(…\)时，得到下列的展开式：
\((x\)\({\,\!}^{2}\)
\(+x+1)\)\({\,\!}^{0}\)
\(=1\) \((x\)\({\,\!}^{2}\)
\(+x+1)\)\({\,\!}^{1}\)
\(=x\)\({\,\!}^{2}\)
\(+x+1\) \((x\)\({\,\!}^{2}\)
\(+x+1)\)\({\,\!}^{2}\)
\(=x\)\({\,\!}^{4}\)
\(+2x\)\({\,\!}^{3}\)
\(+3x\)\({\,\!}^{2}\)
\(+2x+1\) \((x\)\({\,\!}^{2}\)
\(+x+1)\)\({\,\!}^{3}\)
\(=x\)\({\,\!}^{6}\)
\(+3x\)\({\,\!}^{5}\)
\(+6x\)\({\,\!}^{4}\)
\(+7x\)\({\,\!}^{3}\)
\(+6x\)\({\,\!}^{2}\)
\(+3x+1\) \((x\)\({\,\!}^{2}\)
\(+x+1)\)\({\,\!}^{4}\)
\(=x\)\({\,\!}^{8}\)
\(+4x\)\({\,\!}^{7}\)
\(+10x\)\({\,\!}^{6}\)
\(+16x\)\({\,\!}^{5}\)
\(+19x\)\({\,\!}^{4}\)
\(+16x\)\({\,\!}^{3}\)
\(+10x\)\({\,\!}^{2}\)
\(+4x+1\) \(…\)
观察多项式系数之间的关系，可以仿照杨辉三角构造如图所示的广义杨辉三角形，其构造方法：第\(0\)行为\(1\)，以下各行每个数是它头上与左右两肩上的\(3\)个数\((\)不足\(3\)个数的，缺少的数计为\(0)\)之和，第\(k\)行共有\(2k+1\)个数\(.\)若在\((1+ax)(x^{2}+x+1)^{5}\)的展开式中，\(x^{8}\)项的系数为\(75\)，则实数\(a\)的值为\((\) \()\)
