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cot(5x)*cos(x)+sin(x)-sqrt(2)*cos4x=0 equation

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cot(5*x)*cos(x) + sin(x) - \/ 2 *cos(4*x) = 0
$$\left(\sin{\left(x \right)} + \cos{\left(x \right)} \cot{\left(5 x \right)}\right) - \sqrt{2} \cos{\left(4 x \right)} = 0$$
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Numerical answer [src]
x1 = 18.0641577581413
x2 = -42.0188017417635
x3 = 27.8030949842697
x4 = 8.24668071567321
x5 = 26.3108384738145
x6 = -27.8816348006094
x7 = 68.015480950219
x8 = -69.9004365423729
x9 = -48.8517657633213
x10 = -82.0741080750334
x11 = -60.0829594999048
x12 = -61.1039771123215
x13 = -8.32522053201295
x14 = -19.9491133502952
x15 = -100.059726016835
x16 = 71.8639319508665
x17 = -9.8174770424681
x18 = -57.7267650097125
x19 = -5.89048622548086
x20 = 37.856191475757
x21 = 51.9933584169111
x22 = 66.3661448070844
x23 = -17.6714586764426
x24 = -38.0918109247762
x25 = 95.9756555671682
x26 = -36.2853951489621
x27 = 5.89048622548086
x28 = -46.0243323750905
x29 = 30.2378292908018
x30 = 54.1924732744239
x31 = 38.0918109247762
x32 = -56.1559686829176
x33 = 45.9457925587507
x34 = 74.2201264410589
x35 = -61.6537558266997
x36 = -44.3749962319558
x37 = 4.24115008234622
x38 = 48.2234472326033
x39 = -80.2676922992192
x40 = -13.7444678594553
x41 = -35.9712358836031
x42 = 58.2765437240907
x43 = -33.7721210260903
x44 = 56.1559686829176
x45 = 29.3738913110646
x46 = 39.6626072515711
x47 = 60.0829594999048
x48 = 100.138265833175
x49 = 86.0010988920206
x50 = -82.7809664220911
x51 = -4.31968989868597
x52 = -93.7765407096553
x53 = 92.2057443828604
x54 = -63.9314105005523
x55 = 10.2101761241668
x56 = 88.3572933822129
x57 = -53.7997741927252
x58 = 49.872783375738
x59 = 76.5763209312512
x60 = -75.7909227678538
x61 = -21.5984494934298
x62 = -98.5674695063798
x63 = 64.2455697659113
x64 = 84.3517627488859
x65 = -71.8639319508665
x66 = -31.8086256175967
x67 = 70.2931356240716
x68 = 12.1736715326604
x69 = -90.0066295253476
x70 = -77.7544181763474
x71 = 22.3838476568273
x72 = -43.8252175175776
x73 = -2.04203522483337
x74 = 78.3827367070653
x75 = 82.1526478913731
x76 = 16.1006623496477
x77 = 1.96349540849362
x78 = -97.7820713429823
x79 = -10.8384946548848
x80 = 32.5940237809941
x81 = 34.164820107789
x82 = 45.7101731097315
x83 = 89.9280897090078
x84 = -65.5807466436869
x85 = 93.8550805259951
x86 = 24.0331837999619
x87 = 62.0464549083984
x88 = -86.0010988920206
x89 = 41.9402619254237
x90 = 20.2632726156542
x91 = 98.174770424681
x92 = 13.7444678594553
x93 = -39.7411470679109
x94 = -23.7190245346029
x95 = -58.5907029894496
x96 = -16.1792021659874
x97 = -30.0022098417825
x98 = -87.8075146678347
x98 = -87.8075146678347