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Sin^2x+3cos^2x=2sin2x equation

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Numerical solution:

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The solution

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   2           2                
sin (x) + 3*cos (x) = 2*sin(2*x)
$$\sin^{2}{\left(x \right)} + 3 \cos^{2}{\left(x \right)} = 2 \sin{\left(2 x \right)}$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     pi
x1 = --
     4
$$x_{1} = \frac{\pi}{4}$$ 
             /log(10)      /  ____\\          
x2 = -pi + I*|------- - log\\/ 10 /| + atan(3)
             \   2                 /
$$x_{2} = - \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
       /log(10)      /  ____\\          
x3 = I*|------- - log\\/ 10 /| + atan(3)
       \   2                 /
$$x_{3} = \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
           /   ___\
x4 = -I*log\-\/ I /
$$x_{4} = - i \log{\left(- \sqrt{i} \right)}$$ 
x4 = -i*log(-sqrt(i))
Sum and product of roots [src] 
sum
pi           /log(10)      /  ____\\               /log(10)      /  ____\\                  /   ___\
-- + -pi + I*|------- - log\\/ 10 /| + atan(3) + I*|------- - log\\/ 10 /| + atan(3) - I*log\-\/ I /
4            \   2                 /               \   2                 /
$$- i \log{\left(- \sqrt{i} \right)} + \left(\left(\frac{\pi}{4} + \left(- \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)\right) + \left(\operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)\right)$$ 
=
            3*pi        /   ___\       /log(10)      /  ____\\
2*atan(3) - ---- - I*log\-\/ I / + 2*I*|------- - log\\/ 10 /|
             4                         \   2                 /
$$- \frac{3 \pi}{4} - i \log{\left(- \sqrt{i} \right)} + 2 \operatorname{atan}{\left(3 \right)} + 2 i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)$$ 
product
pi /        /log(10)      /  ____\\          \ /  /log(10)      /  ____\\          \ /      /   ___\\
--*|-pi + I*|------- - log\\/ 10 /| + atan(3)|*|I*|------- - log\\/ 10 /| + atan(3)|*\-I*log\-\/ I //
4  \        \   2                 /          / \  \   2                 /          /
$$- i \log{\left(- \sqrt{i} \right)} \frac{\pi}{4} \left(- \pi + \operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right) \left(\operatorname{atan}{\left(3 \right)} + i \left(- \log{\left(\sqrt{10} \right)} + \frac{\log{\left(10 \right)}}{2}\right)\right)$$ 
=
                               /   ___\
pi*I*(pi - atan(3))*atan(3)*log\-\/ I /
---------------------------------------
                   4
$$\frac{i \pi \left(\pi - \operatorname{atan}{\left(3 \right)}\right) \log{\left(- \sqrt{i} \right)} \operatorname{atan}{\left(3 \right)}}{4}$$ 
pi*i*(pi - atan(3))*atan(3)*log(-sqrt(i))/4
Numerical answer [src] 
x1 = 35.806564961886
x2 = -11.7809724509617
x3 = 79.7888621121431
x4 = 89.2136400729125
x5 = -14.4589174955507
x6 = -23.8836954563201
x7 = -64.7243999529874
x8 = 51.5145282298349
x9 = 64.0808988441941
x10 = -80.4323632209364
x11 = 1.24904577239825
x12 = 51.0508806208341
x13 = 86.0720474193227
x14 = -96.1403264888853
x15 = -18.0641577581413
x16 = 73.0420291959627
x17 = 117.487973955221
x18 = -65.1880475619882
x19 = -1.89254688119154
x20 = -1237.00210735098
x21 = 76.1836218495525
x22 = 44.7676953136546
x23 = -62.0464549083984
x24 = -89.8571411817058
x25 = 73.5056768049635
x26 = -67.8659926065772
x27 = -20.7421028027303
x28 = 7.06858347057703
x29 = 95.496825380092
x30 = 67.2224914977839
x31 = 42.0897502690656
x32 = 32.2013246992954
x33 = -33.7721210260903
x34 = 88.7499924639117
x35 = -27.0252881099099
x36 = 10.2101761241668
x37 = 13.8154163867574
x38 = -115.453530019425
x39 = -5.49778714378214
x40 = 22.776546738526
x41 = -93.4623814442964
x42 = -45.8748440314486
x43 = -87.1791961371168
x44 = 82.4668071567321
x45 = 98.174770424681
x46 = 57.7977135370145
x47 = -52.1580293386282
x48 = -253.219959168375
x49 = 38.484510006475
x50 = -86.715548528116
x51 = -30.1668807634997
x52 = -43.1968989868597
x53 = -49.4800842940392
x54 = -27.4889357189107
x55 = -84.037603483527
x56 = 29.5233796547064
x57 = -24613.1293951036
x58 = -36.4500660706793
x59 = 60.4756585816035
x60 = 25.9181393921158
x61 = -55.7632696012188
x62 = 95.0331777710912
x63 = 66.7588438887831
x64 = -36.9137136796801
x65 = -77.7544181763474
x66 = -55.299621992218
x67 = -40.0553063332699
x68 = 3.92699081698724
x69 = 29.0597320457056
x70 = -42.7332513778588
x71 = -58.9048622548086
x72 = 45.2313429226554
x73 = 69.9004365423729
x74 = 20.098601693937
x75 = 54.1924732744239
x76 = 23.2401943475268
x77 = -74.1491779137568
x78 = -14.9225651045515
x79 = -46.3384916404494
x80 = 7.53223107957784
x81 = 16.9570090403472
x82 = -58.4412146458078
x83 = -71.4712328691678
x84 = -99.7455667514759
x85 = 0.785398163397448
x86 = -21.2057504117311
x87 = 16.4933614313464
x88 = -8.17573218837112
x88 = -8.17573218837112
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