Укажите множество корней уравнения

Решите задачу:

$sin^2x\cdot cos^44x=1\; \; \Rightarrow \left \{ {{sin^2x=1} \atop {cos^44x=1}} \right. \; \left \{ {{sinx=\pm 1} \atop {cos^24x=1}} \right. \; \left \{ {{x=\frac{\pi}{2}+\pi n,\; n\in Z} \atop {cos4x=\pm 1}} \right. \\\\ \left \{ {{x=\frac{\pi}{2}+\pi n,\; n\in Z} \atop {4x=\pi m,\; m\in Z}} \right. \; \left \{ {{x=\frac{\pi}{2}+\pi n,\; n\in Z} \atop {x=\frac{\pi}{4}m,\; m\in Z}} \right. \; \Rightarrow \; \; x=\frac{\pi}{2}+\pi n,\; n\in Z$