The value of \(a\in R\) for which the function \(\displaystyle f\left ( x \right )= \left ( 4a-3 \right )\left ( x+\log …

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

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