Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$1 - \cos{\left(x - \frac{\pi}{3} \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{\pi}{3}$$
Numerical solution$$x_{1} = -74.3510266400963$$
$$x_{2} = -68.0678407673484$$
$$x_{3} = -36.6519132139351$$
$$x_{4} = 95.2949767161054$$
$$x_{5} = 57.5958644069028$$
$$x_{6} = -86.9173963246505$$
$$x_{7} = -99.4837675117098$$
$$x_{8} = 13.6135676636004$$
$$x_{9} = 19.8967529723062$$
$$x_{10} = 1.04719798590098$$
$$x_{11} = 13.6135683928511$$
$$x_{12} = 57.5958655509547$$
$$x_{13} = -24.0855441753518$$
$$x_{14} = 70.1622363802125$$
$$x_{15} = 38.7463091427042$$
$$x_{16} = 7.33038320105311$$
$$x_{17} = -11.5191731940441$$
$$x_{18} = 63.8790507175974$$
$$x_{19} = -74.3510259236276$$
$$x_{20} = 7.33038273028594$$
$$x_{21} = 45.0294951410032$$
$$x_{22} = -68.0678392493177$$
$$x_{23} = 19.8967536860244$$
$$x_{24} = -86.9173969295634$$
$$x_{25} = 32.4631239649434$$
$$x_{26} = -11.5191729947456$$
$$x_{27} = -17.8023587550388$$
$$x_{28} = 82.7286070462301$$
$$x_{29} = 82.7286077977356$$
$$x_{30} = 76.4454211240462$$
$$x_{31} = -61.7846550494277$$
$$x_{32} = 32.4631246025263$$
$$x_{33} = -17.8023583238349$$
$$x_{34} = -5.23598787206093$$
$$x_{35} = -30.3687294883483$$
$$x_{36} = -93.2005823302035$$
$$x_{37} = -68.0678413226289$$
$$x_{38} = -49.2182844124382$$
$$x_{39} = -80.6342111126989$$
$$x_{40} = 38.746309893505$$
$$x_{41} = -61.7846558915474$$
$$x_{42} = -5.23598725938577$$
$$x_{43} = 26.1799392376142$$
$$x_{44} = -24.0855436050114$$
$$x_{45} = 63.8790501203265$$
$$x_{46} = 1.0471971836313$$
$$x_{47} = -74.3510267119586$$
$$x_{48} = -36.6519139557788$$
$$x_{49} = 26.1799388484168$$
$$x_{50} = -36.6519147478316$$
$$x_{51} = -30.368728765342$$
$$x_{52} = 26.1799383825674$$
$$x_{53} = 76.4454212081088$$
$$x_{54} = 70.1622355211858$$
$$x_{55} = 101.578161968076$$
$$x_{56} = 13.6135673734423$$
$$x_{57} = 63.8790508072645$$
$$x_{58} = 89.0117914965281$$
$$x_{59} = 70.162236027948$$
$$x_{60} = 51.3126795613314$$
$$x_{61} = -80.6342119022151$$
$$x_{62} = -30.3687296655956$$
$$x_{63} = 19.8967535565785$$
$$x_{64} = -55.5014696969167$$
$$x_{65} = 57.5958648157438$$
$$x_{66} = -93.2005815656485$$
$$x_{67} = 45.0294943400334$$
$$x_{68} = -55.5014703529259$$
$$x_{69} = 95.2949775144473$$
$$x_{70} = 51.3126803577955$$
$$x_{71} = -61.7846554920087$$
$$x_{72} = 38.7463104599544$$
$$x_{73} = -99.483766847019$$
$$x_{74} = 8181.75446884145$$
$$x_{75} = -42.9350991693176$$
$$x_{76} = -11.5191725470651$$
$$x_{77} = -55.5014700888133$$
$$x_{78} = -68.0678405635095$$
$$x_{79} = 7.33038240668485$$
$$x_{80} = 89.011792295987$$
$$x_{81} = 82.7286063004863$$
$$x_{82} = -86.9173971288882$$
$$x_{83} = 32.4631241043919$$
$$x_{84} = -5.23598801500526$$
$$x_{85} = 76.4454217518471$$
$$x_{86} = -24.085543437643$$
$$x_{87} = -42.9350999726765$$
$$x_{88} = -49.2182851726414$$
$$x_{89} = -17.8023579056127$$