Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\left(3 \sin{\left(3 x \right)} - \cos{\left(3 x \right)}\right)^{2} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \frac{2 \operatorname{atan}{\left(- \sqrt{10} + 3 \right)}}{3}$$
$$x_{2} = - \frac{2 \operatorname{atan}{\left(3 + \sqrt{10} \right)}}{3}$$
Numerical solution$$x_{1} = 85.9774494060169$$
$$x_{2} = 24.192793914235$$
$$x_{3} = 20.0040036525658$$
$$x_{4} = 50.3727325789066$$
$$x_{5} = -74.2437759080025$$
$$x_{6} = 13.7208183125049$$
$$x_{7} = 68.1750910862134$$
$$x_{8} = 39.9007571968978$$
$$x_{9} = -52.2526273450963$$
$$x_{10} = 17.9096084463215$$
$$x_{11} = -15.6007131526061$$
$$x_{12} = 6.39043542418929$$
$$x_{13} = 8.48483054311897$$
$$x_{14} = 4.29604035958724$$
$$x_{15} = -19.7895032545139$$
$$x_{16} = 2.20164532951258$$
$$x_{17} = 48.2783375204437$$
$$x_{18} = 46.1839424997665$$
$$x_{19} = -28.1670836207414$$
$$x_{20} = 63.9863008226783$$
$$x_{21} = 17.9096086186406$$
$$x_{22} = 98.5438201090336$$
$$x_{23} = -50.1582321957303$$
$$x_{24} = -23.9782935243469$$
$$x_{25} = 74.4582762530638$$
$$x_{26} = -30.2614787862256$$
$$x_{27} = -89.9517393157849$$
$$x_{28} = -13.5063180229281$$
$$x_{29} = 33.6175719378209$$
$$x_{30} = -87.8573441148333$$
$$x_{31} = 30.4759791114553$$
$$x_{32} = -57.4886151448889$$
$$x_{33} = -85.7629490033135$$
$$x_{34} = -67.9605907133716$$
$$x_{35} = -1.98714493480579$$
$$x_{36} = 81.7886592450701$$
$$x_{37} = 90.1662396735861$$
$$x_{38} = 35.7119668474595$$
$$x_{39} = -48.0638371187664$$
$$x_{40} = -81.574158880264$$
$$x_{41} = 72.3638811567754$$
$$x_{42} = -59.5830103048848$$
$$x_{43} = 52.4671276815611$$
$$x_{44} = -17.6951082204347$$
$$x_{45} = -26.0726885391703$$
$$x_{46} = 94.3550297349574$$
$$x_{47} = -72.1493807711939$$
$$x_{48} = -11.411922911023$$
$$x_{49} = 37.8063621009117$$
$$x_{50} = -92.0461342795111$$
$$x_{51} = 61.8919057747402$$
$$x_{52} = -61.6774053796818$$
$$x_{53} = -63.7718004208548$$
$$x_{54} = 165.564463370126$$
$$x_{55} = 26.287188939878$$
$$x_{56} = 96.4494248256922$$
$$x_{57} = 41.995152238277$$
$$x_{58} = -4.08153996004287$$
$$x_{59} = -39.6862568001909$$
$$x_{60} = -35.4974665859495$$
$$x_{61} = 83.883054352174$$
$$x_{62} = 92.2606346824434$$
$$x_{63} = 59.7975106734356$$
$$x_{64} = 28.38158400137$$
$$x_{65} = -45.9694421168163$$
$$x_{66} = -41.7806518379429$$
$$x_{67} = -8.27033023296453$$
$$x_{68} = -70.054985698865$$
$$x_{69} = 70.2694861012942$$
$$x_{70} = -83.668553958905$$
$$x_{71} = -37.5918617289794$$
$$x_{72} = 15.8152135276435$$
$$x_{73} = -96.2349244738446$$
$$x_{74} = -79.4797636982204$$
$$x_{75} = -87.8573440094279$$
$$x_{76} = -94.1405293471046$$
$$x_{77} = -6.17593504626565$$
$$x_{78} = -76.3381710267172$$