\nfrac{4096}{7016625\pi^4}\!-\! \nfrac{8192}{155925\pi^8} \right) x^{20}    \\[1.5 ex]
        \!\!\!&\!\! \!\!&\!\!\!\!+\! \left(\!-\nfrac{787456}{97692469875}\!+\!\nfrac{512}{2679075\pi^2}\!-\! \nfrac{2048}{127575\pi^4}\!+\!\nfrac{4096}{2835\pi^8} \right) x^{18}           \\[1.5 ex]
        \!\!\!&\!\! \!\!&\!\!\! \!+\! \left(\nfrac{4672}{39092625}\!-\!\nfrac{1024}{297675\pi^2}\!+\!\nfrac{4096}{14175\pi^4}\!-\! \nfrac{8192}{315\pi^8} \right) x^{16}                    \\[1.5 ex]
        \!\!\!&\!\! \!\!&\!\!\!  \!+\! \left(\!-\nfrac{5888}{5108103}\!+\!\nfrac{512}{14175\pi^2}\!-\!\nfrac{2048}{675\pi^4}\!+\!\nfrac{4096}{15\pi^8} \right) x^{14}                       \\[1.5 ex]
        \!\!\!&\!\! \!\!&\!\!\!\!+\! \left(\nfrac{2752}{467775}\!-\!\nfrac{512}{2835\pi^2}\!+\!\nfrac{2048}{135\pi^4}\!-\!\nfrac{4096}{3\pi^8} \right) x^{12}                               \\[1.5 ex]
\!\!\!&\!\! \!\!&\!\!\!\!+\! \left(\!-\nfrac{128}{14175}\!+\!\nfrac{256}{945\pi^2}\!-\! \nfrac{1024}{45\pi^4}\!+\!\nfrac{2048}{\pi^8}\right) x^{10}                                         \\[1.5 ex]
        \!\!\!&\!\!=\!\!&\!\!\! \!-\nfrac{64}{2143861251406875}\nfrac{1}{\pi^8} x^{10} Q_{12}(x).
\end{array}$$ Then, we have to determine sign of the polynomial $$\label{Ineq_63}
\begin{array}{rcl}
Q_{12}(x) \!\!\!&\!\!\!=\!\!\!&\!\!\!(524288\pi^8\!-\!5969040\pi^6\!+\!501399360\pi^4\!-\!45125942400)x^{12} \\[1.25 ex]
\!\!\!&\!\!\!+\!\!\!&\!\!\!(\!-\!13646556\pi^8\!+\!232792560\pi^6\!-\!19554575040\pi^4                       \\[1.25 ex]
\!\!\!&\!\!\!+\!\!\!&\!\!\!1759911753600)x^{10}\!+\!(270011280\pi^8\!-\!6401795400\pi^6                      \\[1.25 ex]
\!\!\!&\!\!\!+\!\!\!&\!\!\!537750813600\pi^4\!-\!48397573224000)x^ {8}\!+\!(\!-\!4003360515\pi^8             \\[1.25 ex]
\!\!\!&\!\!\!+\!\!\!&\!\!\!115232317200\pi^6\!-\!9679514644800\pi^4\!+\!871156318032000)x^{6}                \\[1.25 ex]
\!\!\!&\!\!\!+\!\!\!&\!\!\!(38612227500\pi^8\!-\!1209939330600\pi^6\!+\!101634903770400\pi^4                 \\[1.25 ex]
\!\!\!&\!\!\!-\!\!\!&\!\!\!9147141339336000)x^{4} \!+\!(\!-\!197073451575\pi^8\!+\!6049696653000\pi^6        \\[1.25 ex]
\!\!\!&\!\!\!-\!\!\!&\!\!\!508174518852000\pi^4\!+\!45735706696680000)x^{2}\!\!+\!\!302484832650\pi^8        \\[1.25 ex]
\!\!\!&\!\!\!-\!\!\!&\!\!\!9074544979500\pi^6\!+\!762261778278000\pi^4\!-\!68603560045020000,
\end{array}$$ for $ x\!\in\!(0, 1.53 ]$, which is the polynomial of $12^{th}$ degree. Introducing the substitution $s= x^2$ we can notice that the polynomial $Q_{12}(x)$ can be transformed into polynomial of $6^{th}$ degree $$\label{Ineq_64}
\begin{array}{rcl}
Q_6(s)
\!\!&\!\!\!=\!\!\!&\!\!\left(524288\pi^8\!-\!5969040\pi^6\!+\!501399360\pi^4\!-\!45125942400\right)s^{6}                         \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left(\!-13646556\pi^8\!+\!232792560\pi^6\!-\!19554575040\pi^4\!+\!1759911753600\right)s^{5}              \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left(270011280\pi^8\!\!-\!\!6401795400\pi^6\!\!+\!\!537750813600\pi^4\!\!-\!\!48397573224000\right)s^{4} \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left(\!-4003360515\pi^8\!+\!115232317200\pi^6\!-\!9679514644800\pi^4 \right.                             \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left. 871156318032000\right)s^{3}+\left(38612227500\pi^8\!-\!1209939330600\pi^6 \right.                  \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left. 101634903770400\pi^4\!-\!9147141339336000\right)s^{2}\!+\!\left(\!-\!197073451575\pi^8 \right.     \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!\left. 6049696653000\pi^6\!-\!508174518852000\pi^4\!+\!45735706696680000\right)s                          \\[1.25 ex]
\!\!&\!\!\!+\!\!\!&\!\!302484832650\pi^8\!-\!9074544979500\pi^6\!+\!762261778278000\pi^4                                         \\[1.25 ex]
\!\!&\!\!\!-\!\!\!&\!\!68603560045020000.
\end{array}$$ for $ s\!\in\!(0, 2.3409 ]$. The second derivate of the polynomial $Q_6(x)$ is the polynomial of $4^{th}$ degree $$\label{Ineq_65}
\begin{array}{rcl}
Q_6^{''}(s)\!\!&\!=\!&\!\!30(524288\pi^8-5969040\pi^6+501399360\pi^4-45125942400)s^{4}   \\[1.25 ex]
\!\!&\!+\!&\!\!20(-13646556\pi^8+232792560\pi^6-19554575040\pi^4                         \\[1.25 ex]
\!\!&\!+\!&\!\!1759911753600)s^{3}+12(270011280\pi^8-6401795400\pi^6                     \\[1.25 ex]
\!\!&\!+\!&\!\!537750813600\pi^4-48397573224000)s^{2}+6(-4003360515\pi^8                 \\[1.25 ex]
\!\!&\!+\!&\!\!115232317200\pi^6-9679514644800\pi^4+871156318032000)s                    \\[1.25 ex]
\!\!&\!+\!&\!\!77224455000\pi^8-2419878661200\pi^6+203269807540800\pi^4                  \\[1.25 ex]
\!\!&\!-\!&\!\!18294282678672000.
\end{array}$$ Using MATLAB software 