The range of a$\in$R for which the function f(x) = (4a $-$ 3)(x + log_e 5) + 2(a $-$ 7) cot$\left( {{x \over 2}} \right)$ sin²$\left( {{x \over 2}} \right)$, x $\ne$ 2n$\pi$, n$\in$N has critical points, is :