Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$- \cos{\left(x + \frac{\pi}{3} \right)} - 1 = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{2 \pi}{3}$$
Numerical solution$$x_{1} = 27.2271359067678$$
$$x_{2} = 20.9439514851828$$
$$x_{3} = -92.1533843920784$$
$$x_{4} = 14.6607655022122$$
$$x_{5} = -73.3038280779842$$
$$x_{6} = -4.18879007241912$$
$$x_{7} = 46.0766917994409$$
$$x_{8} = -10.4719752475515$$
$$x_{9} = 33.5103211499068$$
$$x_{10} = -10.4719760031024$$
$$x_{11} = 83.7758040470256$$
$$x_{12} = -67.020642823961$$
$$x_{13} = -16.7551604459813$$
$$x_{14} = -10.4719767770263$$
$$x_{15} = 8.37758023685657$$
$$x_{16} = 64.9262482355789$$
$$x_{17} = -92.1533843813601$$
$$x_{18} = -48.1710872684864$$
$$x_{19} = 83.7758035864127$$
$$x_{20} = 64.926248639561$$
$$x_{21} = -35.6047168806299$$
$$x_{22} = -60.737457602369$$
$$x_{23} = -98.4365709344943$$
$$x_{24} = 102.625360897646$$
$$x_{25} = -29.3215303607458$$
$$x_{26} = -79.5870139950277$$
$$x_{27} = -92.1533850111814$$
$$x_{28} = 83.7758042463573$$
$$x_{29} = 2.0943946568874$$
$$x_{30} = -35.6047168281941$$
$$x_{31} = 58.6430626603427$$
$$x_{32} = -29.321531655846$$
$$x_{33} = 71.2094330621207$$
$$x_{34} = -79.5870133789005$$
$$x_{35} = -48.1710878622247$$
$$x_{36} = -23.0383456693253$$
$$x_{37} = 39.7935069461175$$
$$x_{38} = 8.37758091776503$$
$$x_{39} = 39.7935070870638$$
$$x_{40} = 90.0589892611539$$
$$x_{41} = -98.4365695631877$$
$$x_{42} = 52.3598774913894$$
$$x_{43} = 90.0589889426516$$
$$x_{44} = 96.3421746515371$$
$$x_{45} = -48.1710872321205$$
$$x_{46} = -54.4542738800804$$
$$x_{47} = 27.2271367103103$$
$$x_{48} = -41.8879024849618$$
$$x_{49} = 46.0766926552238$$
$$x_{50} = 96.342174479939$$
$$x_{51} = 71.2094338665045$$
$$x_{52} = 2.09439551638978$$
$$x_{53} = 102.625360739691$$
$$x_{54} = 46.076691931287$$
$$x_{55} = -35.6047162304088$$
$$x_{56} = 58.643063703389$$
$$x_{57} = -29.3215309257509$$
$$x_{58} = 8.37758033149209$$
$$x_{59} = -16.7551612484701$$
$$x_{60} = 1648.28894558793$$
$$x_{61} = -60.7374584035904$$
$$x_{62} = 77.4926180716594$$
$$x_{63} = -79.5870139876991$$
$$x_{64} = 33.5103219101415$$
$$x_{65} = 20.9439506934797$$
$$x_{66} = -29.3215312801435$$
$$x_{67} = -67.020643620102$$
$$x_{68} = -98.4365703086067$$
$$x_{69} = -85.8701987638967$$
$$x_{70} = -85.8701996260547$$
$$x_{71} = 64.9262478503984$$
$$x_{72} = -4.18879015919707$$
$$x_{73} = -4.18879071296507$$
$$x_{74} = 429.35099555528$$
$$x_{75} = -23.0383464633543$$
$$x_{76} = -73.3038288138322$$
$$x_{77} = 77.4926190677516$$
$$x_{78} = -41.8879016233392$$
$$x_{79} = 39.7935064365847$$
$$x_{80} = 14.6607662262999$$
$$x_{81} = 96.3421752130978$$
$$x_{82} = -73.3038274042738$$
$$x_{83} = 33.5103204483135$$
$$x_{84} = 90.058989793089$$
$$x_{85} = 52.3598780656059$$
$$x_{86} = 58.6430633781632$$
$$x_{87} = 14.6607666716224$$
$$x_{88} = -54.4542731559418$$
$$x_{89} = -85.8701989955618$$
$$x_{90} = -41.8879016174728$$
$$x_{91} = 77.4926183030815$$
$$x_{92} = 52.3598773571347$$
$$x_{93} = -54.4542724053277$$