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tgx+3ctgx=2√3 equation

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Numerical solution:

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The solution

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                        ___
tan(x) + 3*cot(x) = 2*\/ 3 
$$\tan{\left(x \right)} + 3 \cot{\left(x \right)} = 2 \sqrt{3}$$
The graph
Sum and product of roots [src]
sum
pi
--
3 
$$\frac{\pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
product
pi
--
3 
$$\frac{\pi}{3}$$
=
pi
--
3 
$$\frac{\pi}{3}$$
pi/3
Rapid solution [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
x1 = pi/3
Numerical answer [src]
x1 = -68.0678407518063
x2 = 82.7286065381173
x3 = 54.4542725558948
x4 = 92.1533846882279
x5 = 4.18879025408787
x6 = 63.8790507661754
x7 = -115.191730505324
x8 = -24.0855435807678
x9 = 82.7286062668862
x10 = 70.162236066459
x11 = -77.4926189206083
x12 = 89.0117916358991
x13 = -2.09439499473715
x14 = 38.7463092946986
x15 = -49.2182851191068
x16 = -27.2271366527141
x17 = 32.4631239765803
x18 = -99.4837675002056
x19 = 38.7463094699634
x20 = -8.37758041826461
x21 = 4.18879027141189
x22 = 16.7551605160766
x23 = -5.2359879252781
x24 = -99.4837676822922
x25 = -71.2094337006472
x26 = -17.8023583177036
x27 = 26.179938863719
x28 = -93.2005822658609
x29 = -93.2005824087029
x30 = 10.4719757215103
x31 = -90.058989336938
x32 = 85.8701993543245
x33 = 98.4365697144432
x34 = -5.23598806814723
x35 = -46.0766920858444
x36 = 19.8967535917185
x37 = -46.0766921664369
x38 = -49.2182852376461
x39 = -39.7935069046144
x40 = -71.2094338229671
x41 = -11.5191731821562
x42 = -55.5014705722673
x43 = -61.784655489932
x44 = 38.7463090999777
x45 = 10.4719753972318
x46 = 60.7374579130517
x47 = 76.4454211351805
x48 = 48.1710874609421
x49 = -27.2271365262547
x50 = 60.7374576835751
x51 = -33.5103217615887
x52 = -83.7758040740577
x53 = 16.7551606819699
x54 = 41.8879021786657
x55 = -55.501470341071
x56 = -11.5191730933126
x57 = -33.5103218486523
x57 = -33.5103218486523