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(2cos2x+sinx–2)√5tgx=0 equation

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Numerical solution:

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The solution

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                            __________    
(2*cos(2*x) + sin(x) - 2)*\/ 5*tan(x)  = 0
$$\sqrt{5 \tan{\left(x \right)}} \left(\left(\sin{\left(x \right)} + 2 \cos{\left(2 x \right)}\right) - 2\right) = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
$$x_{1} = 0$$ 
x2 = pi
$$x_{2} = \pi$$ 
           /    ____    \
           |  \/ 15    I|
x3 = -I*log|- ------ + -|
           \    4      4/
$$x_{3} = - i \log{\left(- \frac{\sqrt{15}}{4} + \frac{i}{4} \right)}$$ 
           /      ____\
           |I   \/ 15 |
x4 = -I*log|- + ------|
           \4     4   /
$$x_{4} = - i \log{\left(\frac{\sqrt{15}}{4} + \frac{i}{4} \right)}$$ 
x4 = -i*log(sqrt(15)/4 + i/4)
Sum and product of roots [src] 
sum
          /    ____    \        /      ____\
          |  \/ 15    I|        |I   \/ 15 |
pi - I*log|- ------ + -| - I*log|- + ------|
          \    4      4/        \4     4   /
$$- i \log{\left(\frac{\sqrt{15}}{4} + \frac{i}{4} \right)} + \left(- i \log{\left(- \frac{\sqrt{15}}{4} + \frac{i}{4} \right)} + \pi\right)$$ 
=
          /    ____    \        /      ____\
          |  \/ 15    I|        |I   \/ 15 |
pi - I*log|- ------ + -| - I*log|- + ------|
          \    4      4/        \4     4   /
$$- i \log{\left(\frac{\sqrt{15}}{4} + \frac{i}{4} \right)} - i \log{\left(- \frac{\sqrt{15}}{4} + \frac{i}{4} \right)} + \pi$$ 
product
     /      /    ____    \\ /      /      ____\\
     |      |  \/ 15    I|| |      |I   \/ 15 ||
0*pi*|-I*log|- ------ + -||*|-I*log|- + ------||
     \      \    4      4// \      \4     4   //
$$- i \log{\left(\frac{\sqrt{15}}{4} + \frac{i}{4} \right)} 0 \pi \left(- i \log{\left(- \frac{\sqrt{15}}{4} + \frac{i}{4} \right)}\right)$$ 
=
0
$$0$$ 
0
Numerical answer [src] 
x1 = 72.2566310325627
x2 = 6.28318530717289
x3 = 84.5703213917823
x4 = -68.8623581238334
x5 = -25.1327412290834
x6 = 9.42477796114735
x7 = -47.1238898022627
x8 = 0.0
x9 = 25.3854214838604
x10 = 31.4159265343836
x11 = 90.8535066989619
x12 = -21.9911485751318 + 4.73209926665986e-13*i
x13 = 97.1366920061415
x14 = -41.0933847518094
x15 = 15.7079632680934
x16 = -85.0756819020665
x17 = -15.707963267953
x18 = -81.6814089933503
x19 = -78.539816339401
x20 = -87.9645943004644 - 1.069202863275e-12*i
x21 = -56.2959875094742
x22 = -50.0128022022946
x23 = 3.1415926543226
x24 = -84.8230016462485
x25 = -28.5270141374502
x26 = 65.9734457253951
x27 = -3.1415926518856
x28 = 46.8712095487048
x29 = 40.8407044985095
x30 = 63.0845333269379
x31 = 40.5880242415252
x32 = 47.1238898046105
x33 = 69.1150383783163
x34 = -34.8101994446298
x35 = 97.3893722616972
x36 = 31.66860679104
x37 = 56.5486677644994
x38 = 88.2172745556563
x39 = 9.1720977056273
x40 = 19.1022361766808
x41 = 18.8495559211906
x42 = -69.1150383793578
x43 = -56.5486677663576
x44 = -24.8800609735763
x45 = -18.8495559222541
x46 = 78.2871360846027
x47 = -18.5968756663967
x48 = 53.1543948558844
x49 = -65.9734457253939 + 1.75797244226204e-12*i
x50 = 15.4552830128069 + 1.07669152850779e-17*i
x51 = 37.9517920982196
x52 = -12.3136903592171
x53 = -3.39427290873187
x54 = 62.8318530714642
x55 = -28.2743338821754
x56 = -34.557519189127
x57 = 59.6902604183625
x58 = 94.2477796076942 + 1.15415751614333e-14*i
x59 = 25.1327412280318
x60 = -62.8318530725416
x61 = -93.9950993525517
x62 = -72.2566310324437
x63 = -53.6597553661686
x64 = -75.3982236863051
x65 = 53.4070751114221
x66 = 84.8230016489267
x67 = -37.6991118430885
x68 = 28.2743338823035
x69 = -91.1061869526251
x70 = -6.03050505203751
x71 = 100.530964914767
x72 = -9.67745821591146
x73 = 44.2349774053992
x74 = -97.6420525164257
x75 = -78.7924965948869
x76 = 91.1061869549002
x77 = -47.376570058989
x78 = 50.2654824574338
x79 = 59.437580163064
x80 = -100.278284659731
x81 = -59.690260418204 + 3.45742071072966e-13*i
x82 = -43.9822971502291 + 6.88498732610723e-12*i
x83 = 2.88891239844771
x84 = -31.4159265360365
x85 = -12.5663706159796
x86 = -91.3588672092461
x87 = 69.3677186341175
x88 = 75.3982236847346
x89 = -75.145543431013
x90 = -62.5791728166538
x91 = 34.3048389343456
x92 = 81.9340892484767
x93 = 12.5663706142316
x94 = 75.6509039412971
x95 = -40.8407044959637
x96 = 21.9911485751317
x96 = 21.9911485751317
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