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sqr(4sin(x+7pi/8))+sqrt(2)*sin2x=1 equation

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Numerical solution:

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The solution

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                       2             
     /    7*pi\     ___              
4*sin|x + ----| + \/ 2  *sin(2*x) = 1
     \     8  /                      
$$\left(\sqrt{2}\right)^{2} \sin{\left(2 x \right)} + 4 \sin{\left(x + \frac{7 \pi}{8} \right)} = 1$$
The graph
Sum and product of roots [src]
sum
0
$$0$$
=
0
$$0$$
product
1
$$1$$
=
1
$$1$$
1
Numerical answer [src]
x1 = 82.2976079246668
x2 = 32.0321254672301
x3 = 44.5984960815893
x4 = 63.448052003128
x5 = -40.5072893380739
x6 = 72.5900461911586
x7 = 3.4750078121832
x8 = -5.6669863758474
x9 = 28.6077490409015
x10 = 53.7404902696199
x11 = -81.0652100620024
x12 = -59.3568452596127
x13 = -84.489586488331
x14 = -53.0736599524331
x15 = 41.1741196552607
x16 = 66.3068608839791
x17 = -659.118258322524
x18 = 88.5807932318464
x19 = -34.2241040308943
x20 = 34.8909343480811
x21 = -68.4988394476433
x22 = 38.3153107744097
x23 = -97.0559571026902
x24 = 6.89938423851177
x25 = 69.7312373103076
x26 = 76.0144226174872
x27 = 107.430349153385
x28 = -46.7904746452535
x29 = 13.1825695456913
x30 = 94.863978539026
x31 = 16.0413784265424
x32 = 60.0236755767995
x33 = -65.6400305667922
x34 = -627.702331786626
x35 = 0.616198931332186
x36 = -9.09136280217597
x37 = -18.2333569902066
x38 = -156.463433748157
x39 = 19.4657548528709
x40 = -21.6577334165351
x41 = 97.722787419877
x42 = -55.9324688332841
x43 = -15.3745481093556
x44 = -445.489957878418
x45 = -24.5165422973862
x46 = 50.8816813887689
x47 = 47.4573049624403
x48 = -71.9232158739718
x49 = 9.75819311936279
x50 = 22.324563733722
x51 = -2.80817749499638
x52 = 57.1648666959485
x53 = -11.950171683027
x54 = -99.9147659835412
x55 = -27.9409187237147
x56 = 25.7489401600505
x57 = -78.2064011811514
x58 = -74.7820247548229
x59 = -37.0829129117453
x60 = -49.6492835261045
x61 = 78.8732314983382
x62 = -30.7997276045657
x63 = -87.348395369182
x64 = 13.1825695456914
x65 = -62.2156541404637
x66 = -93.6315806763616
x67 = 91.4396021126974
x67 = 91.4396021126974