  In this paper, we provide a symmetric formula and a duality formula relating
multiple zeta values and zeta-star values. Leveraging Zagier's formula for
computing $\zeta^\star(\{2\}^p,3,\{2\}^q)$, we employ our theorems to establish
a formula for computing $\zeta^\star(\{2\}^p,1,\{2\}^q)$ for any positive
integers $p$ and $q$, along with other formulas of interest.
