not getting proper solution

i'm trying to solve this question but the solution is in different form, the solution should come as integer.

>> a=30;
>> m=30*pi/180;
>> syms x
>> eq= tan((2*x)-m)==(100-30*sin(x))/(100-30*cos(x));
>> solve(eq,x)

Warning: The solutions are parameterized by the symbols: k, z1. To include parameters and conditions in the solution,
specify the 'ReturnConditions' option. 
> In solve>warnIfParams (line 510)
  In solve (line 360) 
Warning: The solutions are valid under the following conditions: 3*exp(- log(z1) - pi*k*2i) + 3*exp(log(z1) + pi*k*2i)
~= 20 & 2*3^(1/2)*(exp(- log(z1) - pi*k*2i)/2 + exp(log(z1) + pi*k*2i)/2)^2 + 2*(exp(- log(z1) - pi*k*2i)/2 +
exp(log(z1) + pi*k*2i)/2)*((exp(- log(z1) - pi*k*2i)*1i)/2 - (exp(log(z1) + pi*k*2i)*1i)/2) ~= 3^(1/2) & in(k,
'integer') & (z1 == RootOf(z^4 - z^3*(3/20 + 3i/20) - (z*(3^(1/2)*(3 - 3i) - (3 + 3i)))/40 + 3^(1/2)/2 - 1i/2, z)[1] |
z1 == RootOf(z^4 - z^3*(3/20 + 3i/20) - (z*(3^(1/2)*(3 - 3i) - (3 + 3i)))/40 + 3^(1/2)/2 - 1i/2, z)[2] | z1 ==
RootOf(z^4 - z^3*(3/20 + 3i/20) - (z*(3^(1/2)*(3 - 3i) - (3 + 3i)))/40 + 3^(1/2)/2 - 1i/2, z)[3] | z1 == RootOf(z^4 -
z^3*(3/20 + 3i/20) - (z*(3^(1/2)*(3 - 3i) - (3 + 3i)))/40 + 3^(1/2)/2 - 1i/2, z)[4]). To include parameters and
conditions in the solution, specify the 'ReturnConditions' option. 
> In solve>warnIfParams (line 517)
  In solve (line 360) 

ans =

2*pi*k - log(z1)*1i

Answer 1

[Walter Roberson]

plot tan((2*x)-m) - (100-30*sin(x))./(100-30*cos(x)) over a range of values. Do you see any crossings at integral x? If you do, then substitute that x into the equations and see if it is a true solution or only a near solution.

That equation has four real-valued non-rational solutions for every period of 2 Pi.