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√3(cos4x+1)=2(2-cos4x)cos2x equation

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Numerical solution:

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The solution

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              0.333333333333333                            
(cos(4*x) + 1)                  = 2*(2 - cos(4*x))*cos(2*x)
$$\left(\cos{\left(4 x \right)} + 1\right)^{0.333333333333333} = 2 \left(2 - \cos{\left(4 x \right)}\right) \cos{\left(2 x \right)}$$
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Numerical answer [src]
x1 = 46.3431221304638
x2 = 5.5024176337965
x3 = -47.90465747723
x4 = -41.6214721700504
x5 = 10.2055456341525
x6 = 87.1838266271311
x7 = 54.1878427844096
x8 = -54.1878427844096
x9 = 62.0510853984128
x10 = -38.4798795164606
x11 = 76.1789913595381
x12 = 90.3254192807209
x13 = -32.196694209281
x14 = -55.7679000912332
x15 = 47.90465747723
x16 = -29.0551015556912
x17 = -63.612620745179
x18 = -3.92236032697288
x19 = 69.8958060523585
x20 = 98.1701399346667
x21 = -40.0599368232842
x22 = 289.807291803644
x23 = 101.311732588256
x24 = -77.7590486663617
x25 = 84.0422339735413
x26 = 66.7542133987687
x27 = -11.7856029409761
x28 = -19.6303235949218
x29 = -84.0422339735413
x30 = 68.3342707055924
x31 = 25.9135089021014
x32 = -76.1789913595381
x33 = 88.7453619738973
x34 = 18.0687882481557
x35 = -73.0373987059483
x36 = 29.0551015556912
x37 = 4348.74500024166
x38 = -85.6037693203075
x39 = -13.3471382877423
x40 = -62.0510853984128
x41 = 24.3519735553353
x42 = 3.92236032697288
x43 = 8.64401028738629
x44 = -99.7501972414903
x45 = -33.7767515161046
x46 = -69.8958060523585
x47 = -87.1838266271311
x48 = -51.0462501308198
x49 = 2.3608249802067
x50 = -65.1926780520026
x51 = -91.8869546274871
x52 = -25.9135089021014
x53 = 40.0599368232842
x54 = -98.1701399346667
x55 = 113.878103202616
x56 = -82.4621766667177
x57 = -157.860400352873
x58 = 91.8869546274871
x59 = -18.0687882481557
x60 = 32.196694209281
x60 = 32.196694209281