Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(2 x \right)} \cos{\left(2 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{4}$$
$$x_{3} = \frac{\pi}{2}$$
$$x_{4} = \frac{3 \pi}{4}$$
Numerical solution$$x_{1} = -63.6172512351933$$
$$x_{2} = -29.845130209103$$
$$x_{3} = -59.6902604182061$$
$$x_{4} = 86.3937979737193$$
$$x_{5} = -11.7809724509617$$
$$x_{6} = 90.3207887907066$$
$$x_{7} = -87.9645943005142$$
$$x_{8} = -14.1371669411541$$
$$x_{9} = 6.28318530717959$$
$$x_{10} = 18.0641577581413$$
$$x_{11} = -37.6991118430775$$
$$x_{12} = -62.0464549083984$$
$$x_{13} = 91.8915851175014$$
$$x_{14} = 83.2522053201295$$
$$x_{15} = 36.1283155162826$$
$$x_{16} = 0$$
$$x_{17} = -1.5707963267949$$
$$x_{18} = 62.0464549083984$$
$$x_{19} = 40.0553063332699$$
$$x_{20} = 25.9181393921158$$
$$x_{21} = 54.9778714378214$$
$$x_{22} = 87.9645943005142$$
$$x_{23} = 68.329640215578$$
$$x_{24} = -45.553093477052$$
$$x_{25} = 2.35619449019234$$
$$x_{26} = 20.4203522483337$$
$$x_{27} = -69.9004365423729$$
$$x_{28} = 84.037603483527$$
$$x_{29} = -3.92699081698724$$
$$x_{30} = 46.3384916404494$$
$$x_{31} = -65.9734457253857$$
$$x_{32} = -99.7455667514759$$
$$x_{33} = -91.8915851175014$$
$$x_{34} = 65.9734457253857$$
$$x_{35} = -109.170344712245$$
$$x_{36} = -33.7721210260903$$
$$x_{37} = 28.2743338823081$$
$$x_{38} = -25.9181393921158$$
$$x_{39} = -51.8362787842316$$
$$x_{40} = 181.426975744811$$
$$x_{41} = -15.707963267949$$
$$x_{42} = -36.1283155162826$$
$$x_{43} = -95.8185759344887$$
$$x_{44} = 32.2013246992954$$
$$x_{45} = 3.92699081698724$$
$$x_{46} = -47.9092879672443$$
$$x_{47} = -54.1924732744239$$
$$x_{48} = 14.1371669411541$$
$$x_{49} = -84.037603483527$$
$$x_{50} = 95.8185759344887$$
$$x_{51} = -7.85398163397448$$
$$x_{52} = -21.9911485751286$$
$$x_{53} = 64.4026493985908$$
$$x_{54} = -85.6083998103219$$
$$x_{55} = -10.9955742875643$$
$$x_{56} = 21.9911485751286$$
$$x_{57} = 10.9955742875643$$
$$x_{58} = 58.1194640914112$$
$$x_{59} = -32.2013246992954$$
$$x_{60} = 43.9822971502571$$
$$x_{61} = 42.4115008234622$$
$$x_{62} = 54.1924732744239$$
$$x_{63} = 29.845130209103$$
$$x_{64} = 94.2477796076938$$
$$x_{65} = 17.2787595947439$$
$$x_{66} = -55.7632696012188$$
$$x_{67} = 69.9004365423729$$
$$x_{68} = 10.2101761241668$$
$$x_{69} = -73.8274273593601$$
$$x_{70} = -81.6814089933346$$
$$x_{71} = 80.1106126665397$$
$$x_{72} = 24.3473430653209$$
$$x_{73} = -77.7544181763474$$
$$x_{74} = -69.1150383789755$$
$$x_{75} = -18.0641577581413$$
$$x_{76} = -23.5619449019235$$
$$x_{77} = 98.174770424681$$
$$x_{78} = -98.174770424681$$
$$x_{79} = -64.4026493985908$$
$$x_{80} = -80.1106126665397$$
$$x_{81} = -19.6349540849362$$
$$x_{82} = 76.1836218495525$$
$$x_{83} = 7.85398163397448$$
$$x_{84} = -76.1836218495525$$
$$x_{85} = -40.0553063332699$$
$$x_{86} = 51.8362787842316$$
$$x_{87} = -58.1194640914112$$
$$x_{88} = 47.9092879672443$$
$$x_{89} = -41.6261026600648$$
$$x_{90} = -43.9822971502571$$
$$x_{91} = 72.2566310325652$$
$$x_{92} = 73.8274273593601$$
$$x_{93} = 50.2654824574367$$
$$x_{94} = -88.7499924639117$$