Chapter $15,$ Problem $204.$

Two shafts $\backslash ($ A C $\backslash )$ and $\backslash ($ E G $\backslash ),$ which lie in the vertical $\backslash ($ y z $\backslash )$ plane, are connected by a universal joint at $\backslash ($ D $\backslash ).$ Shaft $\backslash ($ A C $\backslash )$ rotates with a constant angular velocity $\backslash (\backslash$omega$\_\{1\}\backslash )$ as shown. At a time when the arm of the crosspiece attached to shaft $\backslash ($ A C $\backslash )$ is vertical, determine the angular velocity of shaft $\backslash ($ E G $\backslash ).$

please see the image and do the clear step$-$by$-$step calculation with explanation and formulas