Complex conjugate poles for OTA unity gain
After doing all the calculations juiciously and going back to the basics of manipulating equations (also from the suggestion from Verbal Kint) I arrived at the following equation
$$
\dfrac{V_o}{V_{in}} = A_0 \cdot \dfrac{s^2 + \dfrac{s}{r_1c_1} + \dfrac{g_{m6} g_{m2}}{c_{in} c_1}}{s^2 + \dfrac{(r_1c_1 + c_{in} r_2)}{r_1r_2c_1c_{in}}s + \dfrac{g_{m6} g_{m2}}{c_{in} c_1}}
$$
where \$ A_0 = \dfrac{g_{m1}g_{m2}r_1r_2}{g_{m1}g_{m2}r_1r_2+1} \$, \$\omega_n= \sqrt{\dfrac{g_{m6}g_{m2}}{c_{in} c_1}}\$, \$ \zeta = \dfrac{ (r_1c_1 + c_{in} r_2)}{2 r_1r_2 \sqrt{c_1c_{in}g_{m6}g_{m2}}} \$. Looks like \$ \zeta \$ will always be less than one and hence there will always be a complex conjugate root present.
a concerned citizen, AJN, Verbal Kint, please can you comment on this answer.