  This article provides a proof that the Ramanujan's Inequality given by,
  $$\pi(x)^2 < \frac{e x}{\log x} \pi\Big(\frac{x}{e}\Big)$$ holds
unconditionally for every $x\geq \exp(59)$. In case for an alternate proof of
the result stated above, we shall exploit certain estimates involving the
Chebyshev Theta Function, $\vartheta(x)$ in order to derive appropriate bounds
for $\pi(x)$, which'll lead us to a much improved condition for the inequality
proposed by Ramanujan to satisfy unconditionally.
