Nope, you're right. 

There's no reason that $\tan \theta$ needs to be less than $1$. You're likely able to check for yourself that $\tan(\pi/3) = \sqrt 3$ (or $\tan(60^\circ)$ if you prefer degrees to radians).

Using sketch to find exact value of trigonometric expression
In Settlers of Catan, I sometimes try to ask people if they want to trade a certain resource, tricking them into revealing the approximate amount of that resource in everyone's hand. After this I play the monopoly card. This has on some occasions not been received very well.

Is this fair play?
