Calculus 1: Optimization Word Problem Messy Algebra

Question

I cannot seem to get the right answer here. The algebra gets very messy.

You are going down a beach that runs north-south. You want to go to a lighthouse 4 miles off the beach at a bearing of 150 degrees. Your car can travel on land and sea. It can go 60mph on the beach and 8mph on water. How far down the beach should you go to minimize the time it takes to get to the lighthouse?

Here is the work I've done. I've attempted it multiple times, but I lose my way in the algebra.

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Answer 1

$T = {l \over 60}+ {w \over 8}$, $w = {4 \sin {\pi \over 6} \over \sin \theta}$, $l = 4 \cos {\pi \over 6} - w \cos \theta$.

$T(\theta) = \frac{2\sqrt{3}\sin \theta −2\cos \theta +15}{60 \sin \theta }$

$T('\theta) = {2 -15 \cos \theta \over 60 \sin^2 \theta}$