Request for closure and/or deletion: https://math.stackexchange.com/questions/4215564/find-lim-x-to0-left-lim-n-to-infty22n-left1-leftf-circ-nx-ri
Very low-quality post. The problem is a classic one: the $x=\cos(\theta)$ sub is the simplest approach exploiting the cosine double-angle formula leading to $\pi^2/16$, yet OP refuses to elaborate and instead "ask for other approaches as it will be helpful to them and others of the community."
I'm amazed the only close vote on it is mine till now (though, with 3 downvotes already).