Determine the exact values of each expression for the given value of $\theta$. Do not use a calculator.
Note: Your answers must be in EXACT form. They cannot contain decimals. If an answer involves a square root, write it as sqrt . For instance, the square root of 2 should be written as sqrt(2).

If $\theta=\frac{\pi}{12}$, then $\tan (2\theta) =$
If $\theta=\frac{\pi}{6}$, then $\cot (2\theta) =$
If $\theta=\frac{5\pi}{2}$, then $\sec (\frac{\theta}{2}) =$
If $\theta=\frac{\pi}{2}$, then $\csc (\frac{\theta}{2}) =$