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sin2x+sinx+cosx=1 equation

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Numerical solution:

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The solution

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sin(2*x) + sin(x) + cos(x) = 1
(sin(x)+sin(2x))+cos(x)=1\left(\sin{\left(x \right)} + \sin{\left(2 x \right)}\right) + \cos{\left(x \right)} = 1
The graph
0-80-60-40-2020406080-1001005-5
Numerical answer [src]
x1 = 43.9822971502571
x2 = -43.9822971502571
x3 = 81.6814089933346
x4 = -31.4159265358979
x5 = 64.4026493985908
x6 = 70.6858347057703
x7 = -25.1327412287183
x8 = 7.85398163397448
x9 = 39.2699081698724
x10 = -94.2477796076938
x11 = -157.07963267949
x12 = 6.28318530717959
x13 = -92.6769832808989
x14 = -23.5619449019235
x15 = -50.2654824574367
x16 = -75.398223686155
x17 = -1036.72557568463
x18 = -56.5486677646163
x19 = -80.1106126665397
x20 = -11359.9990353807
x21 = 50.2654824574367
x22 = -69.1150383789755
x23 = -100.530964914873
x24 = 45.553093477052
x25 = -607.898178469625
x26 = -873.362757697962
x27 = 56.5486677646163
x28 = -62.8318530717959
x29 = -67.5442420521806
x30 = -87.9645943005142
x31 = 18.8495559215388
x32 = 51.8362787842316
x33 = 100.530964914873
x34 = 62.8318530717959
x35 = 94.2477796076938
x36 = 12.5663706143592
x37 = -4.71238898038469
x38 = 95.8185759344887
x39 = -86.3937979737193
x40 = -36.1283155162826
x41 = -17.2787595947439
x42 = 20.4203522483337
x43 = 87.9645943005142
x44 = -48.6946861306418
x45 = 14.1371669411541
x46 = -6.28318530717959
x47 = -73.8274273593601
x48 = 26.7035375555132
x49 = -37.6991118430775
x50 = 89.5353906273091
x51 = -81.6814089933346
x52 = 58.1194640914112
x53 = -61.261056745001
x54 = 37.6991118430775
x55 = 1.5707963267949
x56 = 25.1327412287183
x57 = -42.4115008234622
x58 = 0.0
x59 = -29.845130209103
x59 = -29.845130209103