Custom solution for 3 non-linear simultaneous equations

Solves one type of non-linear system of 3 simultaneous equations in 3 unknowns.

This customised function solves one type of non-linear system
of 3 simultaneous equations in 3 unknowns: k, L and r0 in 3 equations with 4 knowns: zeta, eeta, d and angle.

function matrixresults = symsolvenonlineq(n,degrees,dinput)

% EXAMPLE USAGE: m=symsolvenonlineq(3,45,20)
% nb: takes around 738s to process two 1 x 1000 matrices

INPUT Parameters:
% n determines size of a random matrix for zeta and eeta,
% degrees is the angle and sets constant 'angle' (in radians),
% dinput sets constant 'd'.
%
%OUTPUT:
%returns a 2D matrix of results for k,L and r0.
%
%5 things to note:
%1/ you need to do a 'clear all' prior to running the function
%otherwise it may crash on big input matrices;
%2/ could not use 'zeta' with 'solve' as it gave an error so
%shortened variable 'zeta' to 'zet';
%3/ always produces a complex solution set for k, L and r0.
%4/ always get 2 complex solutions for each of k, L and r0.
%5/ function returns 1 complex solution times n for k, L and r0.