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ctg(x)=(√3/3) equation

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Numerical solution:

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The solution

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cot(x) = -----
           3
cot⁡(x)=33\cot{\left(x \right)} = \frac{\sqrt{3}}{3}
Simplify
Detail solution
Given the equation
cot⁡(x)=33\cot{\left(x \right)} = \frac{\sqrt{3}}{3}
transform
cot⁡(x)−1−33=0\cot{\left(x \right)} - 1 - \frac{\sqrt{3}}{3} = 0
cot⁡(x)−1−33=0\cot{\left(x \right)} - 1 - \frac{\sqrt{3}}{3} = 0
Do replacement
w=cot⁡(x)w = \cot{\left(x \right)}
Expand brackets in the left part
-1 + w - sqrt3/3 = 0

Move free summands (without w)
from left part to right part, we given:
w−33=1w - \frac{\sqrt{3}}{3} = 1
Divide both parts of the equation by (w - sqrt(3)/3)/w
w = 1 / ((w - sqrt(3)/3)/w)

We get the answer: w = 1 + sqrt(3)/3
do backward replacement
cot⁡(x)=w\cot{\left(x \right)} = w
substitute w:
The graph
0-80-60-40-2020406080-100100-2000020000
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
pi
--
3
π3\frac{\pi}{3} 
=
pi
--
3
π3\frac{\pi}{3} 
product
pi
--
3
π3\frac{\pi}{3} 
=
pi
--
3
π3\frac{\pi}{3} 
pi/3
Rapid solution [src] 
     pi
x1 = --
     3
x1=π3x_{1} = \frac{\pi}{3} 
x1 = pi/3
Numerical answer [src] 
x1 = -61.7846555205993
x2 = -83.7758040957278
x3 = -8.37758040957278
x4 = -71.2094334813686
x5 = -90.0589894029074
x6 = 63.8790506229925
x7 = -86.9173967493176
x8 = 95.2949771588904
x9 = -20.943951023932
x10 = 73.3038285837618
x11 = 98.4365698124802
x12 = -39.7935069454707
x13 = 70.162235930172
x14 = -99.4837673636768
x15 = -17.8023583703422
x16 = 13.6135681655558
x17 = 82.7286065445312
x18 = -77.4926187885482
x19 = -80.634211442138
x20 = -42.9350995990605
x21 = -49.2182849062401
x22 = -52.3598775598299
x23 = -14.6607657167524
x24 = 10.471975511966
x25 = 32.4631240870945
x26 = 79.5870138909414
x27 = -55.5014702134197
x28 = -68.0678408277789
x29 = 51.3126800086333
x30 = -46.0766922526503
x31 = 7.33038285837618
x32 = 67.0206432765823
x33 = 41.8879020478639
x34 = 76.4454212373516
x35 = -58.6430628670095
x36 = 54.4542726622231
x37 = 38.7463093942741
x38 = -27.2271363311115
x39 = -5.23598775598299
x40 = 57.5958653158129
x41 = 85.870199198121
x42 = 23.0383461263252
x43 = 60.7374579694027
x44 = 29.3215314335047
x45 = -11.5191730631626
x46 = 4.18879020478639
x47 = 48.1710873550435
x48 = 35.6047167406843
x49 = -30.3687289847013
x50 = -2.0943951023932
x51 = -93.2005820564972
x52 = 92.1533845053006
x53 = -24.0855436775217
x54 = -96.342174710087
x55 = -64.9262481741891
x56 = 16.7551608191456
x57 = 45.0294947014537
x58 = 1.0471975511966
x59 = 26.1799387799149
x60 = -33.5103216382911
x61 = 89.0117918517108
x62 = -36.6519142918809
x63 = 19.8967534727354
x64 = -74.3510261349584
x64 = -74.3510261349584
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