Solve 4sin(2θ)2cos(4θ)=2sin(4θ)

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

Solve for θ

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

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

$$\theta =\pi +arcSin(\frac{1}{8}\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{3}\pi \text{, }n_{3}\in \mathrm{Z}$$

$$\theta =\left(-1\right)arcSin(\frac{1}{8}\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{4}\pi \text{, }n_{4}\in \mathrm{Z}$$

$$\theta =\pi +\left(-1\right)arcSin(\frac{1}{8}\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{5}\pi \text{, }n_{5}\in \mathrm{Z}$$

$$\theta =arcSin(\frac{1}{8}\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{6}\pi \text{, }n_{6}\in \mathrm{Z}$$

$$\theta =\pi +\left(-1\right)arcSin(\left(-\frac{1}{8}\right)\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{7}\pi \text{, }n_{7}\in \mathrm{Z}$$

$$\theta =arcSin(\left(-\frac{1}{8}\right)\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{8}\pi \text{, }n_{8}\in \mathrm{Z}$$

$$\theta =\pi +arcSin(\left(-\frac{1}{8}\right)\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{9}\pi \text{, }n_{9}\in \mathrm{Z}$$

$$\theta =\left(-1\right)arcSin(\left(-\frac{1}{8}\right)\times 22^{\frac{1}{2}}+\frac{1}{8}\times 6^{\frac{1}{2}})+2n_{10}\pi \text{, }n_{10}\in \mathrm{Z}$$