Solve 4sin(4θ)2cos(4θ)=2sin(2θ)

$$4 \sin ( 4 \theta ) 2 \cos ( 4 \theta ) = 2 \sin ( 2 \theta )$$

Solve for θ

$$\theta =\pi n_{1}\text{, }n_{1}\in \mathrm{Z}$$

$$\theta =\frac{1}{2}\pi +\pi n_{2}\text{, }n_{2}\in \mathrm{Z}$$

$$\theta =\pi +2n_{4}\pi +arcSin(\frac{1}{6}\left(18+\left(-6\right)\times 6^{\frac{1}{2}}CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\right)^{\frac{1}{2}})\text{, }n_{4}\in \mathrm{Z}$$

$$\theta =\left(-1\right)arcSin(\frac{1}{6}\left(18+\left(-6\right)\times 6^{\frac{1}{2}}CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\right)^{\frac{1}{2}})+2n_{3}\pi +2\pi \text{, }n_{3}\in \mathrm{Z}$$

$$\theta =\pi +2\pi n_{10}+\left(-1\right)arcSin(\frac{1}{6}\left(18+\left(-6\right)\times 6^{\frac{1}{2}}CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\right)^{\frac{1}{2}})\text{, }n_{10}\in \mathrm{Z}$$

$$\theta =arcSin(\frac{1}{6}\left(18+\left(-6\right)\times 6^{\frac{1}{2}}CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\right)^{\frac{1}{2}})+2\pi n_{9}\text{, }n_{9}\in \mathrm{Z}$$

$$\theta =\pi +arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+9SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{11}\pi \text{, }n_{11}\in \mathrm{Z}$$

$$\theta =\left(-1\right)arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+9SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{12}\pi \text{, }n_{12}\in \mathrm{Z}$$

$$\theta =\pi +\left(-1\right)arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+9SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{13}\pi \text{, }n_{13}\in \mathrm{Z}$$

$$\theta =arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+9SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{14}\pi \text{, }n_{14}\in \mathrm{Z}$$

$$\theta =\pi +arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+\left(-9\right)SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{15}\pi \text{, }n_{15}\in \mathrm{Z}$$

$$\theta =\left(-1\right)arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+\left(-9\right)SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{16}\pi \text{, }n_{16}\in \mathrm{Z}$$

$$\theta =\pi +\left(-1\right)arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+\left(-9\right)SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{17}\pi \text{, }n_{17}\in \mathrm{Z}$$

$$\theta =arcSin(\frac{1}{6}\left(18+3CosI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 6^{\frac{1}{2}}+\left(-9\right)SinI(\frac{1}{3}ArcCosI(\frac{3}{16}\times 6^{\frac{1}{2}}))\times 2^{\frac{1}{2}}\right)^{\frac{1}{2}})+2n_{18}\pi \text{, }n_{18}\in \mathrm{Z}$$