Let's find the inflection points, we'll need to solve the equation for this
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0$$
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
$$\frac{d^{2}}{d x^{2}} f{\left(x \right)} = $$
the second derivative$$2 \left(x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right) = 0$$
Solve this equationThe roots of this equation
$$x_{1} = 100.521017074687$$
$$x_{2} = -72.2427897046973$$
$$x_{3} = 21.945612879981$$
$$x_{4} = 91.0952098694071$$
$$x_{5} = -28.2389365752603$$
$$x_{6} = -50.2455828375744$$
$$x_{7} = -53.3883466217256$$
$$x_{8} = 53.3883466217256$$
$$x_{9} = 56.5309801938186$$
$$x_{10} = -56.5309801938186$$
$$x_{11} = 87.9532251106725$$
$$x_{12} = 97.3791034786112$$
$$x_{13} = 62.8159348889734$$
$$x_{14} = -62.8159348889734$$
$$x_{15} = 40.8162093266346$$
$$x_{16} = 9.31786646179107$$
$$x_{17} = -65.9582857893902$$
$$x_{18} = -37.672573565113$$
$$x_{19} = 69.100567727981$$
$$x_{20} = -75.3849592185347$$
$$x_{21} = 6.12125046689807$$
$$x_{22} = -87.9532251106725$$
$$x_{23} = 84.811211299318$$
$$x_{24} = 12.4864543952238$$
$$x_{25} = -12.4864543952238$$
$$x_{26} = -69.100567727981$$
$$x_{27} = -78.5270825679419$$
$$x_{28} = -43.9595528888955$$
$$x_{29} = -84.811211299318$$
$$x_{30} = 37.672573565113$$
$$x_{31} = 18.7964043662102$$
$$x_{32} = 59.6735041304405$$
$$x_{33} = -91.0952098694071$$
$$x_{34} = 81.6691650818489$$
$$x_{35} = -97.3791034786112$$
$$x_{36} = -40.8162093266346$$
$$x_{37} = 47.1026627703624$$
$$x_{38} = -25.0929104121121$$
$$x_{39} = 78.5270825679419$$
$$x_{40} = -31.3840740178899$$
$$x_{41} = 94.2371684817036$$
$$x_{42} = 25.0929104121121$$
$$x_{43} = -100.521017074687$$
$$x_{44} = 2.79838604578389$$
$$x_{45} = 65.9582857893902$$
$$x_{46} = 34.5285657554621$$
$$x_{47} = -9.31786646179107$$
$$x_{48} = 50.2455828375744$$
$$x_{49} = -34.5285657554621$$
$$x_{50} = -18.7964043662102$$
$$x_{51} = 75.3849592185347$$
$$x_{52} = -21.945612879981$$
$$x_{53} = 15.644128370333$$
$$x_{54} = 43.9595528888955$$
$$x_{55} = 31.3840740178899$$
$$x_{56} = -15.644128370333$$
$$x_{57} = -47.1026627703624$$
$$x_{58} = -94.2371684817036$$
$$x_{59} = -81.6691650818489$$
$$x_{60} = -6.12125046689807$$
$$x_{61} = 28.2389365752603$$
$$x_{62} = -2.79838604578389$$
$$x_{63} = 72.2427897046973$$
$$x_{64} = -59.6735041304405$$
Сonvexity and concavity intervals:Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
$$\left[100.521017074687, \infty\right)$$
Convex at the intervals
$$\left[-2.79838604578389, 2.79838604578389\right]$$