If $\cos e{c}^6\theta -{\cot }^6\theta =a{\cot }^4\theta +b{\cot }^2\theta +c$, then a + b + c =___________

$\begin{array}{l}\cos e{c}^6\theta -{\cot }^6\theta ={\left({\mathrm{cosec}}^2\theta \right)}^3-{\left({\cot }^2\theta \right)}^3\\ =(\cos e{c}^2\theta -{\cot }^2\theta )(\cos e{c}^4\theta +{\cot }^4\theta +\cos e{c}^2\theta {\cot }^2\theta )\\ =1\left[{(1+{\cot }^2\theta )}^2+{\cot }^4\theta +(1+{\cot }^2\theta ){\cot }^2\theta \right]\\ =1+2{\cot }^2\theta +{\cot }^4\theta +{\cot }^4\theta +{\cot }^2\theta +{\cot }^4\theta \\ =3{\cot }^4\theta +3{\cot }^2\theta +1\\ a=3,b=6,c=1\\ \Rightarrow a+b+c=3+3+1=7\end{array}$