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sin(2x)+sqrt(2sin(x)-2sin(x)^3)=0 equation

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Numerical solution:

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The solution

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sin(2*x) + \/  2*sin(x) - 2*sin (x)  = 0
$$\sqrt{- 2 \sin^{3}{\left(x \right)} + 2 \sin{\left(x \right)}} + \sin{\left(2 x \right)} = 0$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
1
$$1$$
=
1
$$1$$
1
Numerical answer [src]
x1 = -83.2522053201295
x2 = 64.4026493985908
x3 = 80.1106126665397
x4 = 29.845130209103
x5 = 10.9955742875643 + 2.91097462232015e-18*i
x6 = -29.845130209103
x7 = 84.2994028713261
x8 = 65.4498469497874
x9 = 15.1843644923507
x10 = 98.9601685880785
x11 = 70.6858347057703
x12 = 4.71238898038469
x13 = 71.733032256967
x14 = -61.261056745001
x15 = 59.1666616426078
x16 = 95.8185759344887
x17 = 58.1194640914112
x18 = -73.8274273593601
x19 = 7.85398163397448
x20 = -28.7979326579064
x21 = -22.5147473507269
x22 = 0.0
x23 = -91.6297857297023
x24 = -89.5353906273091
x25 = 92.6769832808989
x26 = -95.8185759344887
x27 = -14.1371669411541
x28 = -47.6474885794452
x29 = 46.6002910282486
x30 = -51.8362787842316
x31 = -67.5442420521806
x32 = 20.4203522483337
x33 = -32.9867228626928
x34 = -843.517627488859
x35 = 86.3937979737193 + 1.44021703460881e-19*i
x36 = -45.553093477052 + 1.27299593226865e-17*i
x37 = 54.9778714378214
x38 = 23.5619449019235
x39 = 26.7035375555132
x40 = -7.85398163397448
x41 = -60.2138591938044
x42 = 34.0339204138894
x43 = 67.5442420521806
x44 = -1.5707963267949 + 7.55514541112725e-18*i
x45 = -20.4203522483337
x46 = 42.4115008234622 + 1.16047267113722e-18*i
x47 = -72.7802298081635
x48 = -97.9129710368819
x49 = -36.1283155162826
x50 = 51.8362787842316
x51 = -53.9306738866248
x52 = 36.1283155162826
x53 = -58.1194640914112
x54 = -66.497044500984
x55 = 48.6946861306418
x56 = -64.4026493985908
x57 = 78.0162175641465
x58 = -3.66519142918809
x59 = -17.2787595947439
x60 = -104.196156344061
x61 = 40.317105721069
x62 = 73.8274273593601
x63 = -79.0634151153431
x64 = -9.94837673636768
x65 = -23.5619449019235
x66 = -35.081117965086
x67 = -39.2699081698724
x68 = 14.1371669411541
x69 = 21.4675497995303
x70 = -80.1106126665397
x71 = 121.998514714404
x71 = 121.998514714404