If \(\int \left(\frac{1−5{\cos }^{2}x}{{\sin }^{5}x{\cos }^{2}x}\right)dx=f\left(x\right)+C\), where C is the constant o…

If \(\int \left(\frac{1−5{\cos }^{2}x}{{\sin }^{5}x{\cos }^{2}x}\right)dx=f\left(x\right)+C\), where C is the constant of integration, then \(f\left(\frac{\pi }{6}\right)−f\left(\frac{\pi }{4}\right)\) is equal to

[JEE Main 2026, 28 Jan (Shift 1)]