The sum of solutions of the equation \(\frac{\cos x}{1+\sin x}=|\tan 2x|\),\(x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\r…

The sum of solutions of the equation \(\frac{\cos x}{1+\sin x}=|\tan 2x|\),\(x\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)-\left{\frac{\pi }{4},-\frac{\pi }{4}\right}\) is:

[JEE Main 2021, 26 Aug (Shift 1)]