Cutting insert, cutting tool, and method for manufacturing machined product

A cutting insert extending from a front end toward a rear end along a central axis, the cutting insert comprising:

• a cutting portion positioned at a side of the front end and comprising a cutting edge positioned at the front end, and
• a main body portion positioned closer to the rear end than the cutting portion,
• wherein the main body portion comprises an upper surface comprising a first flute, the first flute having a V-shape extending along the central axis, and
• a lower surface positioned on a side opposite from the upper surface, and comprising a second flute, the second flute having a V-shape extending along the central axis,
• wherein the first flute comprises:
• a first region positioned at a side of the rear end, and
• a second region positioned closer to the front end than the first region,
• wherein an opening angle of the first flute in the first region is smaller than an opening angle of the first flute in the second region, and
• wherein an opening angle of the second flute is constant in a direction along the central axis.