The range of \(a\in \mathrm{ℝ}\) for which the function \(f(x)=(4a-3)(x+{\log }_{e}5)+2(a-7)cot\left(\frac{x}{2}\right){…

The range of \(a\in \mathrm{ℝ}\) for which the function \(f(x)=(4a-3)(x+{\log }_{e}5)+2(a-7)cot\left(\frac{x}{2}\right){\sin }^{2}\left(\frac{x}{2}\right)\) \(x\neq 2n\pi ,\mathrm{n}\in \mathrm{ℕ}\), has critical points, is:

[JEE Main 2021, 16 Mar (Shift 1)]