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cot(x+pi/3)=-1 equation

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Numerical solution:

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The solution

You have entered [src] 
   /    pi\     
cot|x + --| = -1
   \    3 /
$$\cot{\left(x + \frac{\pi}{3} \right)} = -1$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     -7*pi
x1 = -----
       12
$$x_{1} = - \frac{7 \pi}{12}$$ 
x1 = -7*pi/12
Sum and product of roots [src] 
sum
-7*pi
-----
  12
$$- \frac{7 \pi}{12}$$ 
=
-7*pi
-----
  12
$$- \frac{7 \pi}{12}$$ 
product
-7*pi
-----
  12
$$- \frac{7 \pi}{12}$$ 
=
-7*pi
-----
  12
$$- \frac{7 \pi}{12}$$ 
-7*pi/12
Numerical answer [src] 
x1 = 64.1408500107916
x2 = 101.839961853869
x3 = 92.4151838930998
x4 = 10.7337748997651
x5 = 82.9904059323304
x6 = -83.5140047079287
x7 = 48.4328867428426
x8 = -36.3901149040818
x9 = -17.540558982543
x10 = 4.45058959258554
x11 = 51.5744793964324
x12 = 70.4240353179712
x13 = -74.0892267471593
x14 = 7.59218224617533
x15 = -14.3989663289532
x16 = -42.6733002112614
x17 = -23.8237442897226
x18 = 73.565627971561
x19 = 76.7072206251508
x20 = 95.5567765466895
x21 = 26.4417381677141
x22 = -4.97418836818384
x23 = 98.6983692002793
x24 = -89.7971900151083
x25 = -61.5228561328001
x26 = -33.248522250492
x27 = 17.0169602069447
x28 = -55.2396708256205
x29 = 1.30899693899575
x30 = 29.5833308213039
x31 = 39.0081087820733
x32 = 86.1319985859202
x33 = -80.3724120543389
x34 = 60.9992573572018
x35 = -77.2308194007491
x36 = 35.8665161284835
x37 = -70.9476340935695
x38 = -48.9564855184409
x39 = 42.1497014356631
x40 = 57.857664703612
x41 = -11.2573736753634
x42 = -26.9653369433124
x43 = 23.3001455141243
x44 = 89.27359123951
x45 = -20.6821516361328
x46 = -8.11578102177363
x47 = -1.83259571459405
x48 = 32.7249234748937
x49 = -30.1069295969022
x50 = -99.2219679758776
x51 = -96.0803753222878
x52 = -86.6555973615185
x53 = -58.3812634792103
x54 = -45.8148928648512
x55 = -92.9387826686981
x56 = 54.7160720500222
x57 = 79.8488132787406
x58 = 20.1585528605345
x59 = -64.6644487863899
x60 = -52.0980781720307
x61 = 13.8753675533549
x62 = -39.5317075576716
x63 = 67.2824426643814
x64 = 45.2912940892529
x65 = -67.8060414399797
x65 = -67.8060414399797
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