Find the curvature of the curve : $ x = t - \sin{t} $ , $y = 1 - \cos{t} $ , $z=4\sin{\dfrac{t}{2}}$.
I have been trying to find the curvature using the formula $ {k_{1}}^2 = \dfrac{{\begin{vmatrix} x''& y'' \\ x' & y' \end{vmatrix}}^2 +{\begin{vmatrix} y'' & z'' \\ y' & z' \end{vmatrix}}^2 + {\begin{vmatrix} z'' & x'' \\ z' & x' \end{vmatrix}}^2}{({x'}^{2}+{y'}^{2}+{z'}^{2})^3}.$