Question: Are Coccothrinax and Aleurites both in the Ephorbiaceae family?

Context paragraphs:
Vernicia: The genus Vernicia, commonly referred to as tung or tung-oil tree, is a genus in the spurge family Euphorbiaceae, first described as a genus in 1790.  It is native to China, Japan, India, and Indochina.  The species have often been included within the related genus "Aleurites".

Aleurites rockinghamensis: Aleurites rockinghamensis, the Candlenut, is a flowering tree in the spurge family, Euphorbiaceae found in northeastern Australia.

Thrinax: Thrinax is a genus in the palm family, native to the wider Caribbean.  It is closely related to the genera "Coccothrinax", "Hemithrinax" and "Zombia".  Flowers are small and bisexual, and are borne on small stalks.

Aleurites moluccanus: Aleurites moluccanus (or "moluccana"), the candlenut, is a flowering tree in the spurge family, Euphorbiaceae, also known as candleberry, Indian walnut, kemiri, varnish tree, nuez de la India, buah keras, or kukui nut tree.

Coccothrinax: Coccothrinax is a genus of palms in the Arecaceae family.  There are more than 50 species described in the genus, plus many synonyms and sub-species.  A new species ("Coccothrinax torrida") has been described as recently as 2006.  Many of the "Coccothrinax" have "silver" or "thatch", or both, in their English common names.  In Spanish-speaking countries, "guano" is a common name applied to the "Coccothrinax" species.  The species are native throughout the Caribbean, the Bahamas, extreme southern Florida and southeastern Mexico, but most of the species are known only from Cuba.

Flueggea neowawraea: Flueggea neowawraea (Mēhamehame) is a species of flowering tree in the Bignay family, Phyllanthaceae, that is endemic to Hawaii.  It can be found in dry, coastal mesic, and mixed mesic forests at elevations of 250 to .  Associated plants include kukui ("Aleurites moluccana"), hame ("Antidesma pulvinatum"), ʻ ahakea ("Bobea" sp.) , alaheʻ e ("Psydrax odorata"), olopua ("Nestegis sandwicensis"), hao ("Rauvolfia sandwicensis"), and aʻ iaʻ i ("Streblus pendulinus").  Mēhamehame was one of the largest trees in Hawaiʻ i, reaching a height of 30 m and trunk diameter of 2 m .  Native Hawaiians used the extremely hard wood of this tree to make weaponry.

Aleurites: Aleurites is a small genus of arborescent flowering plants in the Euphorbiaceae, first described as a genus in 1776.  It is native to China, the Indian Subcontinent, Southeast Asia, Papuasia, and Queensland.  It is also reportedly naturalized on various islands (Pacific and Indian Oceans, plus the Caribbean) as well as scattered locations in Africa, South America, and Florida.

Supporting paragraphs: Coccothrinax Aleurites
Answer: no