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3ctg(x/2-п/4)-√3=0 equation

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Numerical solution:

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The solution

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     /x   pi\     ___    
3*cot|- - --| - \/ 3  = 0
     \2   4 /            
$$3 \cot{\left(\frac{x}{2} - \frac{\pi}{4} \right)} - \sqrt{3} = 0$$
The graph
Sum and product of roots [src]
sum
-5*pi
-----
  6  
$$- \frac{5 \pi}{6}$$
=
-5*pi
-----
  6  
$$- \frac{5 \pi}{6}$$
product
-5*pi
-----
  6  
$$- \frac{5 \pi}{6}$$
=
-5*pi
-----
  6  
$$- \frac{5 \pi}{6}$$
-5*pi/6
Rapid solution [src]
     -5*pi
x1 = -----
       6  
$$x_{1} = - \frac{5 \pi}{6}$$
x1 = -5*pi/6
Numerical answer [src]
x1 = 66.497044500984
x2 = -103.148958792865
x3 = -78.0162175641465
x4 = 97.9129710368819
x5 = 41.3643032722656
x6 = 79.0634151153431
x7 = 72.7802298081635
x8 = -2.61799387799149
x9 = 22.5147473507269
x10 = 60.2138591938044
x11 = -34.0339204138894
x12 = -65.4498469497874
x13 = -46.6002910282486
x14 = 53.9306738866248
x15 = -84.2994028713261
x16 = -71.733032256967
x17 = 35.081117965086
x18 = 3.66519142918809
x19 = -21.4675497995303
x20 = 9.94837673636768
x21 = 16.2315620435473
x22 = -59.1666616426078
x23 = 91.6297857297023
x24 = -15.1843644923507
x25 = 28.7979326579064
x26 = -8.90117918517108
x27 = 85.3466004225227
x28 = -40.317105721069
x29 = 47.6474885794452
x30 = -27.7507351067098
x31 = -52.8834763354282
x32 = -96.8657734856853
x33 = -90.5825881785057
x33 = -90.5825881785057