Solve function is only returning one solution

I am trying to solve a system of 4 equations and 4 unknowns using the matlab solve function. I know that there are several solutions to this system of equations and I need to know more than just the one that is being returned.

syms th13 th14 th15 th16_1 th16_2 w13 w14 w15 w16 a13 a14 a15 a16

r8_4 = 1.8954067;
th8_4 = 105.9929731;
r9_2 = 9.53160604;
th9 = 129.85280129;
r10 = 6.48724184;
th10 = 49.98718547;
r11 = 0.45876947;
th11 = 163.22642382;
r13_1 = 2.231140;
r13 = 5.49701918;
r14 = 4.90813124;
r15 = 4.26848605;
r16_1 = 6.90211437;
r16_2 = 5.58711046;
r17_2 = 4.66865764;
th17 = 141.3590041;
r18 = 6.49056539;
th18 = 103.38347549;
r24 = 6.11345151;
th24 = 67.35451271;

y = 3.57084555;
th16_2 = th16_1 + y;

%% Position Vectors
real_6p_1 = r18*cosd(th18) + r17_2*cosd(th17) + r16_1*cosd(th16_1) + r14*cosd(th14) + r13_1*cosd(th13) == r24*cosd(th24) + r11*cosd(th11) + r10*cosd(th10) + r9_2*cosd(th9) + r8_4*cosd(th8_4);
imag_6p_1 = r18*sind(th18) + r17_2*sind(th17) + r16_1*sind(th16_1) + r14*sind(th14) + r13_1*sind(th13) == r24*sind(th24) + r11*sind(th11) + r10*sind(th10) + r9_2*sind(th9) + r8_4*sind(th8_4);

real_6p_2 = r18*cosd(th18) + r17_2*cosd(th17) + r16_2*cosd(th16_2) + r15*cosd(th15) + r13*cosd(th13) == r24*cosd(th24) + r11*cosd(th11) + r10*cosd(th10) + r9_2*cosd(th9) + r8_4*cosd(th8_4);
imag_6p_2 = r18*sind(th18) + r17_2*sind(th17) + r16_2*sind(th16_2) + r15*sind(th15) + r13*sind(th13) == r24*sind(th24) + r11*sind(th11) + r10*sind(th10) + r9_2*sind(th9) + r8_4*sind(th8_4);

S = solve([real_6p_1 imag_6p_1 real_6p_2 imag_6p_2], [th13 th14 th15 th16_1]);
th13 = vpa(S.th13);
th14 = vpa(S.th14);
th15 = vpa(S.th15);
th16_1 = vpa(S.th16_1);
th16_2 = vpa(th16_1 + y);

Answer 1

[Walter Roberson]

Infinite number of solutions.

syms th13 th14 th15 th16_1 th16_2 w13 w14 w15 w16 a13 a14 a15 a16

r8_4 = 1.8954067;
th8_4 = 105.9929731;
r9_2 = 9.53160604;
th9 = 129.85280129;
r10 = 6.48724184;
th10 = 49.98718547;
r11 = 0.45876947;
th11 = 163.22642382;
r13_1 = 2.231140;
r13 = 5.49701918;
r14 = 4.90813124;
r15 = 4.26848605;
r16_1 = 6.90211437;
r16_2 = 5.58711046;
r17_2 = 4.66865764;
th17 = 141.3590041;
r18 = 6.49056539;
th18 = 103.38347549;
r24 = 6.11345151;
th24 = 67.35451271;

y = 3.57084555;
th16_2 = th16_1 + y;

%% Position Vectors
real_6p_1 = r18*cosd(th18) + r17_2*cosd(th17) + r16_1*cosd(th16_1) + r14*cosd(th14) + r13_1*cosd(th13) == r24*cosd(th24) + r11*cosd(th11) + r10*cosd(th10) + r9_2*cosd(th9) + r8_4*cosd(th8_4);
imag_6p_1 = r18*sind(th18) + r17_2*sind(th17) + r16_1*sind(th16_1) + r14*sind(th14) + r13_1*sind(th13) == r24*sind(th24) + r11*sind(th11) + r10*sind(th10) + r9_2*sind(th9) + r8_4*sind(th8_4);

real_6p_2 = r18*cosd(th18) + r17_2*cosd(th17) + r16_2*cosd(th16_2) + r15*cosd(th15) + r13*cosd(th13) == r24*cosd(th24) + r11*cosd(th11) + r10*cosd(th10) + r9_2*cosd(th9) + r8_4*cosd(th8_4);
imag_6p_2 = r18*sind(th18) + r17_2*sind(th17) + r16_2*sind(th16_2) + r15*sind(th15) + r13*sind(th13) == r24*sind(th24) + r11*sind(th11) + r10*sind(th10) + r9_2*sind(th9) + r8_4*sind(th8_4);

equation = [real_6p_1 imag_6p_1 real_6p_2 imag_6p_2];
vars = [th13 th14 th15 th16_1];

F = matlabFunction(lhs(equation)-rhs(equation), 'vars', {vars});
N = 100;
locs = zeros(N, 4);
opt = optimoptions('fsolve', 'display', 'none');
for K = 1 : N
    x0 = randn(1,4)*1000;
    locs(K,:) = fsolve(F, randn(1,4)*1000, opt);
end
sols = uniquetol(locs,1e-5,'byrows',true);

format long g
sols

sols = 100×4

-2835.82880818841 115.202369757362 1218.95217949277 1122.43616042426 -2475.8288082094 -604.797630229398 858.952179493162 1122.43616040863 -2441.33655450549 -2141.22142845289 -3.69784684434927 -266.002727106797 -2035.45989500304 1167.87803122431 758.874257709475 34.509044905432 -1395.82880807509 -244.797630096013 -1661.04782020201 42.4361603315934 -1395.82878142753 -2764.79759212455 1218.95222174111 -1397.56386728082 -1361.33652904002 2178.77858926081 356.302211414932 -1346.0027378551 -1315.4598951931 87.8780312147776 -681.12574227183 -325.490955082301 -1315.45989402113 447.878030545614 1118.87424357959 -325.490959932525 -1070.02979215949 -675.335881467341 -1355.50833994533 -620.964155232411

[Walter Roberson]

Within the basic range, for at least some of the variables, if x was a solution then so was 360-x