The /Ɵ/ sound is spelled with <th>. The /r/ sound is spelled with <r>, <rr> or <wr>.
This is a contrast between a voiceless dental and alveolar fricative and a voiced continuant, fairly close together in the mouth. It is not a problem, although the individual sounds are difficult for many learners.
Since the /Ɵ/ sound is of low frequency overall, the mean density value is low at 0.4%. The list makes 28 semantic distinctions, a loading of 61%.
Agatha agora author aura authors auras bathing barring Cathy Carrie earthing erring thane rain thanes rains thank rank thanked ranked thanking ranking thanks ranks thatch ratch thatches ratches thaw raw thaw roar thawed roared thaws roars theft reft Thetford Retford thick rick thickets rickets thieve reeve thieves reeves thigh rye thighs rise thing ring things rings thing wring things wrings think rink thinks rinks thole rôle tholes rôles thole roll tholes rolls thong wrong thongs wrongs thought wrought thug rug thugs rugs thumb rum thumbs rums thump rump thumps rumps unearthing unerring
John Higgins, Shaftesbury, November 2010.