Interval of existence of a certain first-order ODE 
Without solving the following initial value problem, determine the interval in which the solution is certain to exist: $$\dfrac{dy}{dx}+(\tan x)y=\sin x, \ \ \ y \left (\frac{\pi}{4} \right )=0.$$

Please help me also solve (if you can) under what conditions the solution of the first-order ordinary differential equation exists?
This question is different is differenr from the previously asked queston in a way that it has two parts furthermore, the equation given is completely different from the previously asked question.
It is sad that none of the repliers have answered the question yet whereas they have accepted that they know answers. I am extremely disappointed with this forum which was suggested to me by my friend. Leaving it right now. Good Bye.

Hint: Multiply the entire equation by $\sec{x}$ and note that
$$\frac{d}{dx}\left[\sec{x}\,y(x)\right]=\sec{x}\,y^\prime{(x)}+\sec{x}\tan{x}\,y(x).$$
