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tg(x-(pi/4))=-(sqrt3)/3 equation

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Numerical solution:

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The solution

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                 ___ 
   /    pi\   -\/ 3  
tan|x - --| = -------
   \    4 /      3   
$$\tan{\left(x - \frac{\pi}{4} \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
The graph
Rapid solution [src]
     pi
x1 = --
     12
$$x_{1} = \frac{\pi}{12}$$
x1 = pi/12
Sum and product of roots [src]
sum
pi
--
12
$$\frac{\pi}{12}$$
=
pi
--
12
$$\frac{\pi}{12}$$
product
pi
--
12
$$\frac{\pi}{12}$$
=
pi
--
12
$$\frac{\pi}{12}$$
pi/12
Numerical answer [src]
x1 = 100.792764302673
x2 = 25.3945406165175
x3 = 53.6688744988256
x4 = -50.0036830696375
x5 = -21.7293491873294
x6 = -84.5612022591253
x7 = -37.4373124552784
x8 = 97.6511716490827
x9 = 9.68657734856853
x10 = 41.1025038844665
x11 = -100.269165527074
x12 = 88.2263936883134
x13 = 3.40339204138894
x14 = 44.2440965380563
x15 = 94.5095789954929
x16 = -59.4284610304069
x17 = -46.8620904160477
x18 = -75.1364242983559
x19 = -12.30457122656
x20 = 12.8281700021583
x21 = 0.261799387799149
x22 = -2.87979326579064
x23 = -31.1541271480988
x24 = -87.7027949127151
x25 = -81.4196096055355
x26 = -97.1275728734844
x27 = -18.5877565337396
x28 = -78.2780169519457
x29 = -68.8532389911763
x30 = -6.02138591938044
x31 = -90.8443875663049
x32 = 50.5272818452358
x33 = 22.2529479629277
x34 = 31.6777259236971
x35 = 63.093652459595
x36 = 19.1113553093379
x37 = 28.5361332701073
x38 = -65.7116463375865
x39 = 34.8193185772869
x40 = -93.9859802198946
x41 = 72.5184304203644
x42 = 91.3679863419031
x43 = 81.9432083811338
x44 = -43.720497762458
x45 = -56.2868683768171
x46 = 69.3768377667746
x47 = -71.9948316447661
x48 = 47.3856891916461
x49 = 6.54498469497874
x50 = 37.9609112308767
x51 = 85.0848010347236
x52 = 15.9697626557481
x53 = -28.012534494509
x54 = 59.9520598060052
x55 = 56.8104671524154
x56 = -40.5789051088682
x57 = 75.6600230739542
x58 = -24.8709418409192
x59 = -34.2957198016886
x60 = -53.1452757232273
x61 = 78.801615727544
x62 = -9.16297857297023
x63 = 66.2352451131848
x64 = -62.5700536839967
x65 = -15.4461638801498
x65 = -15.4461638801498