Sharper Bounds for the Chebyshev function $\theta (x)$

In this article, we provide explicit bounds for the prime counting function $\theta (x)$ in all ranges of $x$. The bounds for the error term for $\theta (x)- x$areoftheshape$\epsilon x$and$\frac{c_k x}{(\log x)^k}$,for$k=1,\ldots,5$\mathrm{.}Tablesofvaluesfor$\epsilon$and$c_k$ are provided.