2023 ONE(c)

The graph shows the curve $y=\frac{2}{(x+1{)}^3}$ , along with the tangent to the curve drawn at $x=1$.

A second tangent to this curve is drawn which is parallel to the first tangent shown in the diagram.

Find the $x$-coordinate of the point where this second tangent touches the curve.

*You must use calculus and show any derivatives that you need to find when solving this problem.*