There are at least 84 solutions, possibly more. Are you expecting to get a closed form solution that lists each of the angles that satisfies the equation? Because that is not going to happen -- trig equations seldom have closed form solutions.
Notice that your cos^2 and sin^2 add up to 1.
And notice that you have cos(45+thtea) instead of cosd(45+thtea) at one point.
syms thtea real
eqn=sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cos(45+thtea)+cosd(45+thtea)*cosd(45+thtea)==0
simplify(eqn)
solve(eqn)
vpasolve(eqn)
fplot([lhs(eqn)-rhs(eqn),0], [-360, 360])
fplot([lhs(eqn)-rhs(eqn),0], [-225, -70])
eqn2 = sind(45)*sind(45+thtea)+sind(45+thtea)*sind(45+thtea)+cosd(45)*cosd(45+thtea)+cosd(45+thtea)*cosd(45+thtea)==0
eqn2 = simplify(eqn2)
sol2 = solve(eqn2, 'returnconditions', true)
sol2.thtea
sol2.conditions
