El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
$$\frac{\left(1 - 2 \cos{\left(2 x \right)}\right) \operatorname{sign}{\left(x - \sin{\left(2 x \right)} \right)}}{\pi} = 0$$
Resolvermos esta ecuaciónPuntos de cruce con el eje X:
Solución numérica$$x_{1} = -63.3554518473942$$
$$x_{2} = -81.1578102177363$$
$$x_{3} = 84.2994028713261$$
$$x_{4} = -87.4409955249159$$
$$x_{5} = -65.4498469497874$$
$$x_{6} = 85.3466004225227$$
$$x_{7} = -68.5914396033772$$
$$x_{8} = 131.423292675173$$
$$x_{9} = 91.6297857297023$$
$$x_{10} = -41.3643032722656$$
$$x_{11} = -97.9129710368819$$
$$x_{12} = 44.5058959258554$$
$$x_{13} = -35.081117965086$$
$$x_{14} = -3.66519142918809$$
$$x_{15} = 2.61799387799149$$
$$x_{16} = -5.75958653158129$$
$$x_{17} = 47.6474885794452$$
$$x_{18} = 30.8923277602996$$
$$x_{19} = -25.6563400043166$$
$$x_{20} = 46.6002910282486$$
$$x_{21} = 19.3731546971371$$
$$x_{22} = -2.61799387799149$$
$$x_{23} = -9.94837673636768$$
$$x_{24} = -47.6474885794452$$
$$x_{25} = 97.9129710368819$$
$$x_{26} = -21.4675497995303$$
$$x_{27} = -62.3082542961976$$
$$x_{28} = -90.5825881785057$$
$$x_{29} = 5.75958653158129$$
$$x_{30} = -18.3259571459405$$
$$x_{31} = 8.90117918517108$$
$$x_{32} = -82.2050077689329$$
$$x_{33} = 66.497044500984$$
$$x_{34} = -2686.58531759487$$
$$x_{35} = -16.2315620435473$$
$$x_{36} = -93.7241808320955$$
$$x_{37} = 75.9218224617533$$
$$x_{38} = 125.140107367993$$
$$x_{39} = 12.0427718387609$$
$$x_{40} = 74.8746249105567$$
$$x_{41} = -85.3466004225227$$
$$x_{42} = 68.5914396033772$$
$$x_{43} = -40.317105721069$$
$$x_{44} = -19.3731546971371$$
$$x_{45} = -34.0339204138894$$
$$x_{46} = -217.293491873294$$
$$x_{47} = 82.2050077689329$$
$$x_{48} = 173.311194723037$$
$$x_{49} = 9.94837673636768$$
$$x_{50} = 60.2138591938044$$
$$x_{51} = 31.9395253114962$$
$$x_{52} = -49.7418836818384$$
$$x_{53} = 63.3554518473942$$
$$x_{54} = 100.007366139275$$
$$x_{55} = 49.7418836818384$$
$$x_{56} = 96.8657734856853$$
$$x_{57} = 25.6563400043166$$
$$x_{58} = 24.60914245312$$
$$x_{59} = 90.5825881785057$$
$$x_{60} = 78.0162175641465$$
$$x_{61} = 38.2227106186758$$
$$x_{62} = -91.6297857297023$$
$$x_{63} = -46.6002910282486$$
$$x_{64} = 53.9306738866248$$
$$x_{65} = 3.66519142918809$$
$$x_{66} = 27.7507351067098$$
$$x_{67} = -31.9395253114962$$
$$x_{68} = -56.025068989018$$
$$x_{69} = 41.3643032722656$$
$$x_{70} = 71.733032256967$$
$$x_{71} = 0$$
$$x_{72} = -53.9306738866248$$
$$x_{73} = -69.6386371545737$$
$$x_{74} = -24.60914245312$$
$$x_{75} = -60.2138591938044$$
$$x_{76} = 16.2315620435473$$
$$x_{77} = -78.0162175641465$$
$$x_{78} = -75.9218224617533$$
$$x_{79} = -12.0427718387609$$
$$x_{80} = 69.6386371545737$$
$$x_{81} = 56.025068989018$$
$$x_{82} = 40.317105721069$$
$$x_{83} = -13.0899693899575$$
$$x_{84} = -38.2227106186758$$
$$x_{85} = -100.007366139275$$
$$x_{86} = -71.733032256967$$
$$x_{87} = -27.7507351067098$$
$$x_{88} = 22.5147473507269$$
$$x_{89} = 34.0339204138894$$
$$x_{90} = -84.2994028713261$$
$$x_{91} = 18.3259571459405$$
$$x_{92} = -43.4586983746588$$
$$x_{93} = 52.8834763354282$$
$$x_{94} = 93.7241808320955$$
$$x_{95} = 62.3082542961976$$
$$x_{96} = 88.4881930761125$$