$a=\frac{-2i}{entd^{3}\sin(x)\left(\left(1+i\right)e^{ix}+\left(-1+i\right)e^{-ix}\right)}$
$\nexists n_{1}\in \mathrm{Z}\text{ : }\left(x=\pi n_{1}+\frac{3\pi }{4}\text{ or }x=\pi n_{1}\right)\text{ and }d\neq 0\text{ and }t\neq 0\text{ and }n\neq 0$

$\left\{\begin{matrix}d=\sqrt[3]{4}a^{-\frac{1}{3}}n^{-\frac{1}{3}}t^{-\frac{1}{3}}\times \left(2i\sin(x)\right)^{-\frac{1}{3}}\left(\left(1+i\right)e^{ix+1}+\left(-1+i\right)e^{-ix+1}\right)^{-\frac{1}{3}}\text{, }&\nexists n_{2}\in \mathrm{Z}\text{ : }\left(x=\pi n_{2}+\frac{3\pi }{4}\text{ or }x=\pi n_{2}\right)\text{ and }a\neq 0\text{ and }t\neq 0\text{ and }n\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }x=\pi n_{1}\\d=-2^{\frac{2}{3}}e^{\frac{\pi i-1}{3}}a^{-\frac{1}{3}}n^{-\frac{1}{3}}t^{-\frac{1}{3}}\times \left(2i\sin(x)\right)^{-\frac{1}{3}}\left(\left(1+i\right)e^{ix}+\left(-1+i\right)e^{-ix}\right)^{-\frac{1}{3}}\text{; }d=2^{\frac{2}{3}}ie^{\frac{\pi i-2}{6}}a^{-\frac{1}{3}}n^{-\frac{1}{3}}t^{-\frac{1}{3}}\times \left(2i\sin(x)\right)^{-\frac{1}{3}}\left(\left(1+i\right)e^{ix}+\left(-1+i\right)e^{-ix}\right)^{-\frac{1}{3}}\text{, }&\nexists n_{2}\in \mathrm{Z}\text{ : }\left(x=\pi n_{2}+\frac{3\pi }{4}\text{ or }x=\pi n_{2}\right)\text{ and }a\neq 0\text{ and }t\neq 0\text{ and }n\neq 0\end{matrix}\right.$