Representation of data — practice question

Particle $P$ is travelling inside a smooth hollow cone with its vertex pointing downward and its axis vertical, and the semi-vertical angle is $45^\circ$. A light inextensible string, parallel to the cone’s surface, links $P$ to the vertex. $P$ moves at constant angular speed in a horizontal circle of radius $0.67\,\text{m}$ (see diagram). The string tension is equal to the weight of $P$.