(1) Use the quotient and reciprocal identities to express $\displaystyle {\sec{\theta}}$ in terms of $\displaystyle {\csc{\theta}}$ and $\displaystyle {\tan{\theta}}$:

$\displaystyle {\sec{\theta}}=$   

(type "theta" for $\displaystyle \theta$)

(2) Now, use the identity generated above and that:

 $\displaystyle {\csc{\theta}}=\frac{{23}}{{18}}$ 

 $\displaystyle {\tan{\theta}}=\frac{{{18}\sqrt{{{205}}}}}{{205}}$ 

to find the value of $\displaystyle {\sec{\theta}}$ exactly. Be sure to express your final answer as a rationalized fraction of lowest terms.

 $\displaystyle {\sec{\theta}}=$