Theta of a put option formula

\[ \theta = -\frac{S\phi\left ( d1 \right )\sigma}{2\sqrt{t}}+rKe^{-rt}N\left ( -d2 \right ) \\ {\small where: \phi\left ( d1 \right ) = \frac{e^{-\frac{d1^{2}}{2}}}{\sqrt{2\pi}} } ; \] \[ {\small d1 = \frac{ln \left( \frac{S}{K} \right ) + \left(r+\frac{\sigma^{2}}{2}\right)t}{\sigma\sqrt{t}} ; } \] \[ {\small d2 = d1 - \sigma \sqrt{t}} \ \]