  The inverse tangent function can be bounded by different inequalities, for
example by Shafer's inequality. In this publication, we propose a new sharp
double inequality, consisting of a lower and an upper bound, for the inverse
tangent function. In particular, we sharpen Shafer's inequality and calculate
the best corresponding constants. The maximum relative errors of the obtained
bounds are approximately smaller than 0.27% and 0.23% for the lower and upper
bound, respectively. Furthermore, we determine an upper bound on the relative
errors of the proposed bounds in order to describe their tightness
analytically. Moreover, some important properties of the obtained bounds are
discussed in order to describe their behavior and achieved accuracy.
