Question: What time period was the war that the tribe of Native Americans historically living on the plains of Colorado and Wyoming fought in against the United States?

Context paragraphs:
Arapaho music: The Arapaho are a tribe of Native Americans from the western Great Plains, in the area of eastern Colorado and Wyoming.  Traditional Arapaho music, described by Bruno Nettl (1965, p. 150), includes sacred and secular songs.  Traditional music uses terraced descent type melodic motion, with songs consisting of two sections, each with a range of more than an octave and scales of four to six tones.

Colorado orogeny: The Colorado orogeny, or Colorado orogen, was an orogeny in Colorado and surrounding areas which was a part of the development of the ancestral Rockies.  The Colorado orogeny, formerly called the Colorado province, is a >500-km-wide belt of oceanic arc rock (1.78–1.65 Ga) that extends southward into New Mexico and composes a major part of the Proterozoic provinces of southwestern United States.  This transcontinental collisional event occurred during the Paleoproterozoic (Statherian Period).  The Wyoming sector of the Colorado orogeny was formerly called the Medicine Bow orogeny.  The eastern sector extends into the High Plains and is called the Central Plains orogeny.  The boundary between the Colorado orogeny and the Wyoming craton is the Cheyenne belt, a 5-km-wide mylonitic shear zone that verges northward.  The Cheyenne belt transects and cuts off the south edge of the older Trans-Hudson orogeny.

Indigenous languages of Arizona: Arizona, a state in the southwestern region of the United States of America, is known for its high population of Native Americans.  Arizona has the third highest number (and the sixth highest percentage) of Native Americans of any state in the Union (See Demographics of Arizona).  Out of the entire US population of 2.9 million Native Americans, roughly 286,680 live in Arizona, representing 10% of the country's total Native American population.  Only California and Oklahoma have more Native Americans than Arizona by number.  Arizona also has the highest proportion of land allocated to Native American reservations, at 28%.  Arizona has five of the twelve largest Indian reservations in the United States, including the largest, the Navajo Nation, and the third-largest, the Tohono O'odham Nation.  Also, Arizona has the largest number of Native American language speakers in the United States.

Native Americans in the American Civil War: Native Americans in the American Civil War saw Native American individuals, bands, tribes, and nations participate in numerous skirmishes and battles.  Native Americans served in both the Union and Confederate military during the American Civil War.  They were found in the Eastern, Western, and Trans-Mississippi Theaters.  At the outbreak of the war, for example, the majority of the Cherokees sided with the Union, but soon after allied with the Confederacy.  Native Americans fought knowing they might jeopardize their sovereignty, unique cultures, and ancestral lands if they ended up on the losing side of the Civil War.  28,693 Native Americans served in the Union and Confederate armies during the Civil War, participating in battles such as Pea Ridge, Second Manassas, Antietam, Spotsylvania, Cold Harbor, and in Federal assaults on Petersburg.

Major Crimes Act: The Major Crimes Act (U.S. Statutes at Large, 23:385) is a law passed by the United States Congress in 1885 as the final section of the Indian Appropriations Act of that year.  The law places certain crimes under federal jurisdiction if they are committed by a Native American in Native territory.  The law follows the 1817 General Crimes Act, which extended federal jurisdiction to crimes committed in Native territory but did not cover crimes committed by Native Americans against Native Americans.  The Major Crime Act therefore broadened federal jurisdiction in Native territory by extending it to some crimes committed by Native Americans against Native Americans.  The Major Crimes Act was passed by Congress in response to the Supreme Court of the United States's ruling in "Ex parte Crow Dog" (109 U.S. 556 (1883)) that overturned the federal court conviction of Brule Lakota sub-chief Crow Dog for the murder of principal chief Spotted Tail on the Rosebud Indian Reservation.

Buffalo jump: A buffalo jump is a cliff formation which Native Americans historically used to hunt and kill plains bison in mass quantities.

Red Cloud's War: Red Cloud's War (also referred to as the Bozeman War or the Powder River War) was an armed conflict between the Lakota, Northern Cheyenne, and Northern Arapaho on one side and the United States in Wyoming and Montana territories from 1866 to 1868.  The war was fought over control of the western Powder River Country in present north-central Wyoming.  This grassland, rich in buffalo, was traditionally Crow Indian land, but the Lakota had recently taken control.  The Crow tribe held the treaty right to the disputed area, according to the major agreement reached at Fort Laramie in 1851.  All involved in "Red Cloud's War" were parties in that treaty.

Indian removal: Indian removal was a policy of the United States government in the 19th century whereby Native Americans were forcibly removed from their ancestral homelands in the eastern United States to lands west of the Mississippi River, thereafter known as Indian Territory.  In a matter that remains one of debate by scholars, description of the policy—which clearly contributed to devastation in numbers, freedom and prosperity for those displaced—is sometimes elevated to being one of long-term genocide of Native Americans, in any case, a consequence of actions first by European settlers to North America in the colonial period, then by the United States government and its citizens until the mid-20th century.  The policy traced its direct origins to the administration of James Monroe, though it addressed conflicts between European Americans and Native Americans that had been occurring since the 17th century, and were escalating into the early 19th century as white settlers were continually pushing westward.  The Indian Removal Act was the key law that forced the removal of the Indians, and was signed into law by President Andrew Jackson on May 28, 1830.

Alcohol and Native Americans: Native Americans in the United States have historically had extreme difficulty with the use of alcohol.  Problems continue among contemporary Native Americans; 12% of the deaths among Native Americans and Alaska Natives are alcohol-related.  Use of alcohol varies by age, gender and tribe with women, and older women in particular, being least likely to be regular drinkers.  Native Americans, particularly women, are more likely to abstain entirely from alcohol than the general US population.  Frequency of use among Native Americans is generally less than the general population, but the quantity consumed when it is consumed is generally greater.

Arapaho: The Arapaho ( ; in French: "Arapahos, Gens de Vache") are a tribe of Native Americans historically living on the plains of Colorado and Wyoming.  They were close allies of the Cheyenne tribe and loosely aligned with the Lakota and Dakota.  The Arapaho language, "Heenetiit", is an Algonquian language closely related to Gros Ventre (Ahe/A'ananin), whose people are considered to have separated from the Arapaho at an early time.  The Blackfeet and Cheyenne also speak Algonquian languages, but theirs are quite different from Arapaho.

Supporting paragraphs: Red Cloud's War Arapaho
Answer: 1866 to 1868