9) Show that tan30 + 1/tan30 = 1/sin30cos30

So, for this I just subbed in the appropriate trig ratios and solved it to get 2.3, which is the same for both. However, the answer in the book has it as 4√3/3. I know this equals the same thing, but I'm not sure how to get it in that format...Could someone show and explain the steps? Thanks! (: