I need to find the minimum value of $c$,
If the equation, $\sec\theta+\csc\theta=c$ has two real roots between $0$ and $2\pi$.
My attempt:
I converted the trig ratio in terms of sine and cosine and got $\sin\theta+\cos\theta=c\cos\theta\sin\theta$. Squaring this gives a quadratic equation in $\sin2\theta$, $c^2\sin^22\theta-4\sin2\theta-4=0.$ How to proceed further?