Find the volume of a regular triangular pyramid, apothem of which = b, and makes an angle

Find the volume of a regular triangular pyramid, apothem of which = b, and makes an angle α with the area of the base of the pyramid.

The volume is calculated by the formula: V = h * a ^ 2/4 roots of 3. Find the height of the pyramid from a right-angled triangle formed by the height, apothem and base: sinα = h / b => h = sinα * b.
The height drops to the center of the base – a point equidistant from all the peaks. That is, h1 = 2 * h * cosα = 2sinα * b * cosα, where h1 is the height of the base of the pyramid. Angles at the base of the triangle = 60 degrees. ctg60 = (a / 2) / h1. Hence a = 2 * h1 * ctg60. Substitute in the formula V = sinα * b * (2 * 2 * sinα * b * cosα * ctg60) ^ 2 / 4√3 = 4b ^ 3 * sinα ^ 3 * cosα ^ 2 / 3√3.