3. Given that
$$2 \cos ( x + 50 ) ^ { \circ } = \sin ( x + 40 ) ^ { \circ }$$
- Show, without using a calculator, that
$$\tan x ^ { \circ } = \frac { 1 } { 3 } \tan 40 ^ { \circ }$$
- Hence solve, for \(0 \leqslant \theta < 360\),
$$2 \cos ( 2 \theta + 50 ) ^ { \circ } = \sin ( 2 \theta + 40 ) ^ { \circ }$$
giving your answers to 1 decimal place.