Given that
$$2 \cos ( x + 30 ) ^ { \circ } = \sin ( x - 30 ) ^ { \circ }$$
without using a calculator, show that
$$\tan x ^ { \circ } = 3 \sqrt { 3 } - 4$$
(4)
Hence or otherwise solve, for \(0 \leqslant \theta < 180\),
$$2 \cos ( 2 \theta + 40 ) ^ { \circ } = \sin ( 2 \theta - 20 ) ^ { \circ }$$
Give your answers to one decimal place.
(3)