Ninth degree analogue of Ramanujan's septic theta function identity

On page 206 in his lost notebook, Ramanujan recorded a seventh degree identity for his theta function $\phi (q)$. We give an analogous ninth degree identity. We also provide an application of an entry from his second notebook on a cubic equation and an interpretation with theta functions for some of his trigonometric identities. Lastly, we calculate five examples for $\phi (e^{-\pi \sqrt{n}})$.