Equivalent Impedance using Matrix, Eigen value and Eigen vector, norm

I am solving this below problem(attachment 1). How to find the exp(theta1) and exp(theta2)...?

1. Attachment pdf.pdf is the problem I am trying to solve.
2. Attachment Tzeng_2006_J._Phys._A__Math._Gen._39_8579.pdf is the theory

Y11 =1-1i/sqrt(3);        Y12 =1i/sqrt(3);         Y13 =-1;            
Y21 =1i/sqrt(3);          Y22 =0;                  Y23 =-1i/sqrt(3);           
Y31 =-1;                  Y32 =-1i/sqrt(3);        Y33 =1+1i/sqrt(3);              
Y11 = Y12 + Y13 ; Y22 = Y21 + Y23 ; Y33 = Y31 + Y32 ; 


L = [Y11, Y12, Y13; Y21, Y22, Y23;  Y31, Y32, Y33];

[EVector,EValue] = eig(L'*L) ;                     % V = Values % D = VECTORS
Sigma_2 = sqrt(EValue(2,2))
Sigma_3 = sqrt(EValue(3,3))

[John D'Errico]

You already know how to use eig. It returns all of the eigenvalues, and their associated eigenvectors.

Throw away all of the eigenvalues that are negative, as well as the eigenvectors associated with the ones you don't want. Toss any that are complex too, if that is a problem. What remains are the non-negative eigenvalues, as well as their eigenvectors.

So where is the problem?

[RAJA KUMAR]

I want all of my eigen values to be nonnegative

[Walter Roberson]

Q = @(v) sym(v);

Y11 = 1-1i/sqrt(Q(3));        Y12 = 1i/sqrt(Q(3));         Y13 = Q(-1);            
Y21 = 1i/sqrt(Q(3));          Y22 = Q(0);                  Y23 = -1i/sqrt(Q(3));           
Y31 = -1;                     Y32 = -1i/sqrt(Q(3));        Y33 = 1+1i/sqrt(Q(3));              
Y = [Y11, Y12, Y13; Y21, Y22, Y23;  Y31, Y32, Y33;  Y41, Y42, Y43]

Unrecognized function or variable 'Y41'.

A = L'*L    ;           % e = eig(L_P*L);
[V,EVC] = eig(A)                     % V = Values % D = VECTOR