What method should be used to solve the following nonlinear simultaneous equations for $z_1, z_2, z_3$
$$a_2z_1^2 + a_1z_2^2 - (z_1z_2 \tan(t))^2 - z_1z_2 2b_1/\cos(t)^2 = b_1/\cos(t)^2 - a_1a_2$$
$$a_3z_2^2 + a_2z_3^2 - (z_2z_3 \tan(t))^2 - z_2z_3 2b_2/\cos(t)^2 = b_2/\cos(t)^2 - a_2a_3$$
$$a_1z_3^2 + a_3z_1^2 - (z_3z_1 \tan(t))^2 - z_3z_1 2b_3/\cos(t)^2 = b_3/\cos(t)^2 - a_3a_1$$
where $a_1,a_2,a_3,b_1,b_2,b_3,t$ are known.
Any help would be appreciated.
