I strongly recommend that you practise deriving the Sine Rule as part of your plan/strategy to memorise it.
The derivation involves constructing an altitude of a triangle (to create two right-angled triangles), writing out trigonometric ratios for each small triangle, and then solving equations simultaneously. These are all skills worthy of attention.
Performing this derivation is an exercise that should take you less than two minutes per day. This is very effective study!
When studying triangles that do NOT contain a right angle, there are three trigonometric formulae that we should know: the Sine Rule, the Cosine Rule, and the Area Rule. Interestingly, they all derive from the same diagram.
In this video I explain how to derive and learn the Sine Rule. At a later date I will produce at least one video explaining how to recognise when to use the rule ... and how to use it.